Using Fractal Thinking to Determine Consumer Patterns Necessary for Organizational Performance: An Approach Based on Touchpoint Pilot Modeling

Abstract

This study models customer patterns using fractal analysis and examines how touchpoints and customer journey mapping shape value to enhance sustainable organizational and customer performance. The analysis is made at cell-level using mathematical modelling and tactical indicators within a top-three retail organization with national presence. This study reveals that only half of the customers engage with multiple touchpoints, with specific departments experiencing low interaction levels. The company’s customer concentration is well-balanced, reducing dependency on a single client, and mutual dependency suggests robust customer–company sustainable relationships. Results underline the significance of the proposed tools in evaluating the value of the customers for the company. Practical implications include guiding managers to use modelling in strengthening customer touchpoints to enhance qualitative relationships and profitability. This research contributes to customer relationship management and fractal analysis literature, demonstrating their role in maximizing bi-directional value and performance for success.

1. Introduction

According to the ‘give and get’ principle, the need to build sustainable relationships with customers became a condition of bi-directional value co-creation and performance for organizations. By treating customers the right way and by monitoring them, the company may gain competitive advantage using new different patterns specific for fractal analysis to improve their relationship with customers [1]. Thus, benefits could be obtained by analyzing the sentiments of customers, the engagement dynamics, the interactions with the firms, the degree of acceptance, the interaction with the brand, the companies, and their employees [2], the new products and processes [3], new value co-creation and experiences, customized solutions [4], loyalty and satisfaction [5,6], branding strategies [7], business sustainability through digital technologies [8], sustainable strategies based on corporate agility and customer capability [9], corporate social responsibility and goals based on sustainable consumption and production [10], environmental prosocial attitudes based on green consumption and relationship with customers [11], sustainable businesses based on using AI in their relationship with the environment and customers [12], and, of course, improving their relationship with Generation Z in this digital era [13]. Fractal analysis helps to create path consistency between shoppers and companies [14] by influencing consumer decisions using patterns [15] or fitting experimental data to realistic data of consumers for approximate estimations [16].

A customer is the only one who brings value to an organization, so a user-centric customer support service is vital to be developed in companies [17] and to find creative solutions [18] by using mathematical modelling, economic analysis, and evaluation of reviews and sentiments [19].

This analysis will improve the relationships of companies with their customers, based on engagement, awareness, customer orientation through continuous innovation [20], cognitive presence, analyzing intentions, affective social interactions, positive attitudes to shop [21], intention to buy based on attractiveness, affinity, emotional connection, experience, and customer journey [22], effective and mutual interactions [23], relationship, customer information and knowledge [24], and influencing marketing strategies [25,26] based on physical and virtual platforms as omnichannel touchpoints tools [27,28] for digital interaction and engagement [29] and inverted U-shaped relationships [30].

The consumers can meet the company goals based on customer journeys and touchpoints, as moments of truth [31]. Omnichannel communication, virtual platforms, and social media all became important touchpoints in contemporary customer journeys [32].

The touchpoints reach them through experience, with its music, like an orchestra [33]. The touchpoint is a journey based on value, utility, and memories for customers, and for the organization, it is a story based on information, data, and knowledge. The two stories join to create a new one based on trust, involvement, and a two-way relationship. Touchpoints are critical to organizational performance and customer performance [34].

The novelty of this research is consisting in the determination of customers’ pattern using fractal analysis to build and maintain profitable relationships with customers. Another element of novelty is that using tactical indicators and touchpoints indicate their importance at cell-level for determining the value of profitable customers and observe the impact could have on organization and customer benefits.

This study contributes to the existing literature by adding the growing body of literature on managerial consequences of using fractal analysis in customer relations management. It will also bring to light the understanding of the indicators used to analyze the value of a customer, enriching the literature on the perceptions linked by the importance of a valuable customer based on a continuous relationship.

This paper is organized as follows: Section 2 presents the literature review, highlighting the definitions of customer value based on customer journey mapping and touchpoint and tactical indicators, using Share of Wallet (SOW), Size of Wallet (SW), Share of Category Requirement (SCR), customer concentration (CC), mutual dependency (MD), and Spearman’s test. Section 3 presents the research methodology, the objectives, and analysis. Section 4 presents the pattern determination based on using tactical indicators to establish customer journey mapping and the intensity of a valuable customer or of a visited department in an organization. Discussion and conclusions based on the research and the results obtained are presented, and the final part describes limitations and future research directions. As a result of using modelling and simulation, the experts may observe the risks that might occur in the relationship with customers, which could affect the performance of the organization based on relationships with its customers.

2. Literature Review

There are few studies using fractal analysis, so this study can be very important to fulfill the theoretical existing gap in the field. Thus, fractal analysis was used in a few papers (only 20 studies based on Web of Science analysis) in determining customer behavior patterns, such as the following: movement of customers in retail and determining the classification of customers using Gaussian function [35], shopping paths to determine a relationship between customer movement and their sales [36], customer segmentation and marketing optimization [37] and the risk for rational consumption [38], the relationship between consumer spending and financial market volatility during the COVID-19 period in South Korea [39], and trust in brands and consumer behavior in Taiwan [40].

A few indicated that fractal analysis could bring real benefits for technical quality (constancy and utilization of new technologies), functional quality (reliability, usefulness, receptiveness for consumers and supervisors), and strategic value (high, medium or low), with the high value offering a competitive advantage for the company [41].

Other studies show that, by using fractal analysis, the company may determine the consumption of limited resources in their relationship with customers, the natural relationships or volatility, uncertainty, complexity, and ambiguity of the customer relationship, and diversity [42] based on fractal surfaces [43,44].

According to this analysis, other studies are necessary to fill this gap; thus, our literature review is divided into two parts: one based on a description of customer journey mapping and touchpoint intensity and the other based on a presentation of tactical indicators used to determine the value of a profitable customer and a pattern for organizational performance.

2.1. Customer Journey Mapping and Touchpoint Intensity

Customer experience throughout the customer journey is a vital element for companies. Multichannel touchpoints make customer experiences more social [45]. Customer experience management will allow firms to overcome competition; it will help us understand customer perceptions, customer needs, and use specific metrics to adequately manage these experiences [46]. To improve interactions with customers, the companies must not fragment the use of customer experiences, customer journey mapping, and touchpoints [47]. Two studies made by an international team show the positive effect of customer experience on customer engagement [48]. Experiences may be physical or virtual; a meta-analysis made among over 19,000 respondents from 62 independent studies demonstrated that online customer experience reduced emotions [49], and emotions concerning interaction and innovation are very important as was demonstrated in 25 interviews conducted by an international team [50].

Customer journey mapping illustrates the experience of a customer and the moment of interaction [51], being a valuable and flexible service design tool that helps the company to see from their perspective. It is important to examine each interaction due to the used touchpoints resulting from complex customer journeys and multiple channels. Customer experience depends on customer journey mapping [52], which may be physical or digital, and is called a physical journey [53]. The company must properly map its destination using adequate tools, the focus being not on a specific technique but value alignment. To have an adequate customer journey map, it is important to determine the unique characteristics of the segment [54]. More complex and dynamic journeys enrich consumer decision-making [55].

To understand customer behavior better, the marketers must examine and structure the touchpoints [56] and their phases [57]: detail the consumer journey and individual touchpoints and assess internal design requirements, efforts, activities, and specialists. The customer enters the relationship reacting to different touchpoints, leading to better product recognition, information collection, information processing, receiving personalized services, and building databases, which must be clear, unique, constantly updated, and completed.

The touchpoint may be the following:

-

Positive (empathy, curiosity, imagination, objectivity) [58], neutral [59] or negative (dissatisfaction, lack of communication, of orientation, or of awareness) [60].

-

Direct (face to face) or indirect (phone, email, call centers, newspapers, websites) [55,61].

-

Physical (personal interactions, sensorial meetings based on human touches and special fragrance), or digital (telesales, helpdesk, mobile applications, email, online ads, social media, billboards, music apps or free apps) [62,63].

All the presented touchpoints may help organizations to better understand the customer’s behaviour and their value for organizations interested in achieving sustainable performance.

In today’s relationship world, cross-channel attribution is a very interesting topic, optimizing marketing initiatives and using advanced analytics to allocate proportional credit to more than one channel or touchpoint [64].

The company–customer relationship is an important key factor of interactive marketing, and its role is to generate bi-directional value [65] and mutual economic benefits [66]. In this era, customers, which have increased, are gaining more power; the firms are reducing the prices and, implicitly, their performance. Customers are the source of obtaining venue and developing enterprise innovation, stimulating creativity [67]. To determine the value of customers, we analyzed some indicators to determine the influence of a final touchpoint on performance.

There are a few models used in multi-touch marketing [64]:

• Linear attribution—Each touchpoint of the customer receives equal credit to the final purchase; if there are five channels, each receives 20% in the final purchase.
• U-shaped—In this model, some channels are more important than others. The most important are the first and the last touch, receiving 40%, and the others an equal weight.
• W-shaped—From the total channels, the model considers some more important (first, middle, and last) and the others not. The core ones receive 30% and the others 5% credit.
• Time decay—In this model, more importance is offered to the ones found closer to the final purchase. Last-touch attribution works well for digital campaigns because the customer actions happen so quickly after the campaign [68], which is the reason for analyzing this type of touchpoint in our study.

Studies demonstrated that, to have a positive touchpoint, analysis of the following variables is important:

a 

The characteristics of using a touchpoint:

-

For customers [69]: empathy, curiosity, imagination, objectivity, and self awareness;

-

For companies: networking abilities [64], communication, and value [70].

b 

The benefits resulting from using a touchpoint:

-

For the organization: easy transfer of experience into the new touchpoint in sustainability and moral norms [71] to create, maintain, or design high-quality touchpoint combinations [72], business smarts and awareness, natural leadership, ability to influence, to persuade, to follow, or to be flexible, raw talent to create something new, and speed, accuracy, connection to brand, the skills of the selling team, the visual marketing tools, and authenticity through the use of AI for young generations [70].

-

For the customer: trust, social benefits, knowing their own needs better, preferences and desires, customization, minimal risks [73,74,75], increased satisfaction, special treatment, and performance [34].

To determine a customer journey and a touchpoint implicitly, a different analysis was made to identify the touchpoint and the channel used for contacts, necessary to determine a certain pattern for customers’ shopping processes. The results indicated that the more points there are, the greater the involvement in purchasing the product [55]. A study conducted on 2970 B2B customers demonstrated that human and physical touchpoints led to more increased outcomes than the digital ones, requiring greater attention from retailers [31]. Among 543 German respondents, a study was conducted in which the preference of customers for in-person or online touchpoints was analyzed, demonstrating that this is an important attribute in choosing a certain service [76]. Digital touchpoints need more attention and more skills to manage and control a digital touchpoint and more focus on managing resources, actions, and a digital environment [77]. Personalization of customer experiences and of touchpoints (nature, design, stage) are influencing customer performance and organization performance, which is stated in a study reviewing 293 articles conducted in the field [34]. Omnichannel touchpoints have an important effect on customer experience and intention of shopping [27]. A study conducted on 309 respondents highlighted the importance of various variables for effective touchpoints, such as authenticity, media richness, brand attitude, and perception [78]; inspiration, engagement, involvement, feedback, information, tolerance, and strong relationships [79]; the use of pre-cycling information and knowledge, implications, and recycling efforts for recycled packaging [71]; and identity, value, status, and socialization in both real and virtual touchpoints [80]. Additionally, a study involving 1112 respondents revealed that loyalty, experience, attention, autonomy, competence, and relationships enhance face-to-face or virtual touchpoints, creating more and higher-quality touchpoint combinations [72], using analyses based on PLS-SEM (SmartPLS 4.1.1.4.), SPSS, or AMOS software. It was demonstrated among 444 young customers that perceived authenticity acts as a mediator between media richness (AI and chatbots) and value co-creation [70]. Research conducted on over 4500 respondents from Iran, using CFA and PLS-SEM, demonstrated that social, hedonic, and utilitarian shopping values have a positive effect on the effectiveness of real and virtual touchpoints [81].

Other studies have demonstrated that using SPSS, PLS-SEM, or interviews that study the interaction between companies and customers may bring important mutual benefits [80,81], such as the following: dialog, motivation, satisfaction, hedonic value, effective online experiences [64,68,69,72,73,82], interactive content, brand–consumer interaction, brand co-building [74,75,83], interactive decisions through socializing processes, reduced service time, good prices, utility [34,70,72,74,84], influence on customer emotions by reducing fear, anxiety, risks, and uncertainty through pleasant customer experiences [85], influence on satisfaction through increased perceived service quality [71,86], emotion valence, involvement, and effective interactions [50].

2.2. Touchpoint Indicators and the Value of a Customer

Customers have contact with companies in many ways, and companies must know how to keep and work with valuable customers; organizations might use strategic indicators or tactical indicators. Using these indicators the companies may determine the customer value and experience of valuable and loyal customers.

From the tactical indicators we remind the reader of the following:

Size of Wallet (SW)—The total amount spent by a customer on a category of products; according to this indicator, the company may determine the target segment, the transactional and relational value, and the development of specific interactive strategies [87]. Using this indicator, the company may also determine patterns for shopping and their expenditures among competitors [84]. A larger SW indicates more revenues and profits [52].

The SW formula is as follows:

$$SW=Sj{\sum }_{j=1}^J.$$

(1)

where J = the firm, and ${\sum }_{j=1}^J.$ = the number of sales.

Share of Wallet (SOW)—Defined as the percentage of a customer’s total category expenditure captured by the firm [88]. It measures the amount spent on a brand, compared to other brands. It is used to understand better the customer characteristics, profile, needs, relationship duration, and interactions [88].

Its formula of calculation is as follows:

$${\mathrm{SOW}}_{ \mathrm{individual} \%} = {\displaystyle \frac{{\mathrm{S}}_{\mathrm{i}}}{\sum {\mathrm{S}}_{\mathrm{i}}}}$$

(2)

where S = the value of sales made in a firm, and ∑S_i = the number of sales made in all the firms.

Gegory Requirement (SCR)—Defined as the proportion of the volume of sales made by a customer in the total volume of the brand.

The formula of calculation is as follows:

$$\mathrm{SCR} = {\displaystyle \frac{\mathrm{Vij}}{{\sum }_{\mathrm{j}=1}^{\mathrm{J}}\mathrm{Vij}}} \times 100$$

(3)

where V_ij = the volume of individual sales, i = individual who buys, j = all the firms from a category of brands, and ${\sum }_{\mathrm{j}=1}^{\mathrm{J}}{\mathrm{V}}_{\mathrm{i}\mathrm{j}}$ = the total volume of the bought category [52].

Customer concentration (CC)—Indicates a company’s degree of dependence upon customers, and it is a measure of competitive structure [89]. The literature in the field shows that there is a direct relationship between CC and strategic decisions, customers’ profitability, customer engagement and repurchase intentions, and risk [90,91] or innovation capability. Valuable customers have the motivation and power to monitor their suppliers’ product quality and financial status, creating a customer–supplier win-win situation [92]. Customer power facilitates collaboration, and both parties may benefit. CC is negatively associated with the supplier’s firm profitability; however, it is positively associated with the valuable customers’ profitability. CC should evenly spread revenues across customers because valuable customers improve efficiency and provide access to resources. The results suggest that a 10% increase in CC reduces profitability by 3.35%.

Previous studies have shown that CC is a double-edged sword, which may lead to the following:

-

A negative impact: A greater CC will lower the customer credit quality [93], offer customers stronger bargaining powers [94], higher costs and financial risks of the company, low purchase quantity, and reduce loyalty among consumers [95],

-

A positive impact: A greater CC will lead to higher profitability, provide stable sales channels, and guarantees efficiency, significant cash flow, and efficient production. Because the company has an asymmetric dependence on influential customers, losing them would result in a crisis for the company.

CC may be 1 if a supplier has at least one customer and 0 otherwise [92]. To measure CC, two indicators are used: CC₅ and CCHH₅ [96].

CC₅ is the degree of CC and it is determined by summing up the sales of the top five customers divided by the total sales:

$${\mathrm{CC}}_5={\sum }_{\mathrm{j}=1}^5\left({\displaystyle \frac{{\mathrm{Sales}}_{\mathrm{ij}}}{{\mathrm{Sales}}_{\mathrm{i}}}}\right)$$

(4)

CCHH₅ or the Herfindahl–Hirschman index of CC is determined by the square of each top five customer’s sales on total sales:

$${\mathrm{CCHH}}_5={\sum }_{\mathrm{j}=1}^5{\left({\displaystyle \frac{{\mathrm{Sales} \mathrm{to} \mathrm{customer}}_{\mathrm{ij}}}{{\mathrm{Sales}}_{\mathrm{i}}}}\right)}^2$$

(5)

Thus, the higher the proportion of the top five customer’s sales is, the higher the CC. CC is about the number of major customers and the relative importance of each major customer. Relying on a few major customers exposes firms to lower profit margins and higher risks resulting from bankruptcies and walk-outs [93].

Mutual dependency (MD)—When CC is high, the company and the customers may become mutually dependent [97], thereby affecting their business strategies. Thus, due to the asymmetric relationship, the suppliers face a high degree of cash flow risk or face low switching costs, therefore increasing their relative bargaining position.

Mutual dependency is measured in a three-step process: define the dependence of the company i on customer j as the customer importance in the company’s annual sales (S_ij); define the dependence of the customer j annual purchases (P_ij); and measure the symmetric mutuality of dependence between the company and using (S_ij × P_ij) in line.

Its formula is as follows:

$$\mathrm{MD} = {\sum }_{\mathrm{j}=1}^{\mathrm{j}}\left[{\mathrm{w}}_{\mathrm{ij}}({\mathrm{S}}_{\mathrm{ij}} \times {\mathrm{P}}_{\mathrm{ij}})\right]$$

(6)

where

$${\mathrm{w}}_{\mathrm{ij}}=\left({\displaystyle \frac{{\mathrm{Sales}}_{\mathrm{ij}}}{{\mathrm{Sales}}_{\mathrm{i}}}}\right)/{\sum }_{\mathrm{j}=1}^{\mathrm{j}}\left({\displaystyle \frac{{\mathrm{Sales}}_{\mathrm{ij}}}{{\mathrm{Sales}}_{\mathrm{i}}}}\right)$$

(7)

and

$${\mathrm{S}}_{\mathrm{ij}}={\displaystyle \frac{{\mathrm{Sales}}_{\mathrm{ij}}}{{\mathrm{Sales}}_{\mathrm{i}}}}$$

(8)

and

$${\mathrm{P}}_{\mathrm{ij}}=\left({\displaystyle \frac{{\mathrm{Sales}}_{\mathrm{ij}}}{{\mathrm{Cost} \mathrm{of} \mathrm{goods} \mathrm{sold}}_{\mathrm{j}}}}\right)$$

(9)

The ij Sales represent the i sales to customer i, the Sales i represent the companies’ total sales, and the Cost of goods sold j denotes customer total purchase from all the companies. The MD values range between 0 and 1, where higher values indicate greater MD between the company and its major customers [91].

Spearman’s test (r)—This indicator is not part of tactical indicators but is used to measure the correlation between variables; Spearman’s test may be used as it shows how well this relationship can be described by a monotonic function [98]. If it is 1, there is a perfect positive correlation, and if it is −1, there is a perfect negative correlation; 0 means no correlation.

The formula used is as follows [99]:

$$\mathrm{r} = 1 -{\displaystyle \frac{6 \times \sum {\mathrm{d}}^2}{\mathrm{n} \times ({\mathrm{n}}^2-1)}}$$

(10)

3. Research Methodology

Goal—This study models customer patterns using fractal analysis and examines how touchpoints and tactical indicators shape the value of customers for organizations. The research was carried out on customers from an organization demonstrating retail activity (building materials and home and garden decoration products), with activity studied on the national level. According to the official statistics, the company is among the top three companies in Romania.

Objectives—To measure the value of a customer using specific tools, such as the following: SOW, SW, SCR, CC, MD, Spearman’s test, customer journey maps, and the intensity of a touchpoint (for customers and departments), using GeoGebra apps and simulation techniques. The model used for analysis was based on the last-touch attribution or the exposure in the moment of purchase.

Methods of research—Time decay or last-touch attribution, direct method (face-to-face discussion), physical interaction, and observation were applied on a sample at cell-level (10 respondents), shoppers from the analyzed organization, and modelling (fractal analysis to observe a pattern in the shopper’s behavior).

Sample—The respondents were chosen on different days among the customers willing to discuss if they bought some products, and the criteria used was the amount comprised between 150 m.u. and 1000 m.u. to avoid the large differences between them. They were asked to remember the total amount spent on products and the sum spent on each product. The responses are shown in

Table 1. Data on the analyzed customers and SW calculation (m.u.).

Customer/Dep	A	B	C	D	E	F	G	SW
1	30	37.69	37.99	18.28	12	0	15	150.96
2	94.46	35.58	54.63	43.4	181.87	0	0	409.94
3	37.6	64.5	134.21	79.58	0	0	0	315.89
4	23.98	46.7	45.61	105	104.28	0	26	351.57
5	127.59	50.3	85.58	25.64	0	0	0	289.11
6	47.25	78.46	227.4	31.04	0	0	53.4	437.55
7	13.62	24.98	79.17	33.14	196.36	0	0	347.27
8	77.41	36.26	52.23	35.19	0	0	0	201.09
9	0	0	240	0	0	200	236	676
10	0	0	0	0	0	175	0	175
Total	451.91	374.47	956.82	371.27	494.51	375	330.4	3354.38

Note: A—thermal, sanitary, electrical, sewage, and gas installations (TSESG), B—materials for construction (MFC), C—materials for interior design (MFID), D—tools, accessories, equipment (TAE), E—garden (G), F—furniture (F), G—electronics and home appliances (EHA).

.

4. Results

Our study proposed to analyze customer journey mapping and measure customer value using touchpoint indicators and to observe the influence of touchpoints on organizational and customer benefits and performance.

We used cell-level research, with the goal to expand the calculations in future research for different industries or using different test models. Choosing a cell-level study reflects that the use of more respondents would have increased the number of pages of the article through the tables used, and the graphic representation of the data would have been much wider, making it difficult for the interested parties to understand the process. The study is perceived as a pilot, adequate to start other studies; for example, determining patterns for more customers, for more companies, or industries, areas, or more models used. The study took place in February–March 2025, and only 10 customers with a purchase value of over 150 monetary units (m.u.) were chosen for analysis. The total value written on the tax receipt was divided between departments (which is denoted from A–G as below) and then between the customers (from 1 to 10) (Table 1). When they declared the purchase sum, they were asked to specify to which wage category they belonged, a question necessary to determine the mutual dependency indicator.

4.1. Tactical Indicators and the Value of a Customer

These tactical indicators are used to determine the valuable customers for the analyzed company (Table 1 and

Table 2. SOW for the analyzed customers.

Customer/Dep	A	B	C	D	E	F	G
	SOW	SOW	SOW	SOW	SOW	SOW	SOW
1	0.2	0.25	0.25	0.12	0.08	0	0.1
2	0.23	0.09	0.13	0.11	0.44	0	0
3	0.12	0.2	0.42	0.25	0	0	0
4	0.07	0.13	0.13	0.3	0.3	0	0.07
5	0.44	0.17	0.3	0.09	0	0	0
6	0.11	0.18	0.52	0.07	0	0	0.12
7	0.04	0.07	0.23	0.1	0.57	0	0
8	0.38	0.18	0.26	0.17	0	0	0
9	0	0	0.36	0	0	0.3	0.35
10	0	0	0	0	0	1	0

).

The highest SW was recorded by customers 9 (676 m.u.), 6 (437.55 m.u.), 2 (409.94 m.u.), 4 (351.57 m.u.), 7 (347.27 m.u.), 3 (315.89 m.u.), 5 (289.11 m.u.), 8 (201.09 m.u.), 10 (175 m.u.), and 1 (150.96 m.u.). Thus, the most valuable customers for the analyzed organization are customers 9, 6, 2, and 4; therefore, the relationship must be improved. Concerning the others, the transactional relation might be used.

Analyzing the value of each department in the total value of a customer, the greatest values of SOW are recorded for department A, customers 5 (0.44), 8 (0.38) and 2 (0.23); for department B, customers 1 (0.25), 6 (0.18), and 8 (0.18); for C, customers 6 (0.52), 3 (0.42), and 9 (0.36); for D, customers 4 (0.3), 3 (0.25), and 8 (0.17); for E, customers 7 (0.57), 2 (0.44), and 4 (0.3); for F, customers 9 (0.3) and 10 (1); and for G, customers 9 (0.35), 6 (0.12), and 4 (0.07) (Table 2).

Here, the highest SOW values registered are mentioned in department E (customer 7 with 0.57), department C (customer 6 with 0.52), and department E (customer 2 with 0.44).

So, investing in departments for design and garden materials is important to obtain a long-term relationship. It is also important to create an attractive atmosphere and invest in relationship skills for employees to collaborate better with valuable customers.

Measuring the value of each customer for each department in total value, the greatest SCRs are shown for A: customers 1 (0.066), 5 (0.038), and 2 (0.028); for B: customers 6 (0.21), 3 (0.17), and 5 (0.13); for C: customers 9 (0.25), 6 (0.24), and 3 (0.14); for D: customers 4 (0.28), 3 (0.21), and 2 (0.12); for E: customers 7 (0.4), 2 (0.37), and 4 (0.21); for F: customers 9 (0.53) and 10 (0.47), and for G: customers 9 (0.71), 6 (0.16), and 4 (0.08) (

Table 3. SCR for the analyzed customers.

Customer/Dep	A	B	C	D	E	F	G
	SCR	SCR	SCR	SCR	SCR	SCR	SCR
1	0.066	0.1	0.04	0.05	0.02	0	0.05
2	0.028	0.1	0.06	0.12	0.37	0	0
3	0.011	0.17	0.14	0.21	0	0	0
4	0.007	0.12	0.05	0.28	0.21	0	0.08
5	0.038	0.13	0.09	0.07	0	0	0
6	0.014	0.21	0.24	0.08	0	0	0.16
7	0.004	0.07	0.08	0.09	0.4	0	0
8	0.023	0.1	0.05	0.09	0	0	0
9	0	0	0.25	0	0	0.53	0.71
10	0	0	0	0	0	0.47	0

).

Here, the highest SCR values registered are mentioned in department G (customer 9 with 0.71), department F (customer 9 with 0.53), and department F (customer 10 with 0.47).

So, investing in products for garden and furniture is important to obtain a profitable relationship with customers. Also, investing in the development for relational and communication skills for employees is important to attract and retain valuable customers and influence them to buy products.

From these calculations, we may say that tactical indicators are important tools in determining how a valuable customer is determined and create plans to improve future relationships.

4.2. Customer Journey Mapping, Touchpoint Intensity, and the Value of a Customer

Analyzing the customers’ journeys, customers’ experience at each department, and the mapping of each journey, the heatmap of a department can be established (

Table 4. Customer’ experience mapping by departments.

Customer	The Route Colour	Touchpoints (Departments)	No of Touchpoints
1	Red	A, B, C, D, E, G	6
2	Yellow	A, B, C, D, E	5
3	Blue	A, B, C, D	4
4	Green	A, B, C, D, E, G	6
5	Orange	A, B, C, D	4
6	Grey	A, B, C, D, G	5
7	Mauve	A, B, C, D, E	5
8	Light green	A, B, C, D	4
9	Brown	C, F, G	3
10	Pink	G	1
Total			43

).

The most increased number of touchpoints are recorded by customers 1 and 4 (with six touchpoints), then by customers 2, 6, and 7 (with five touchpoints), then by customers 3, 5, and 8 (with four touchpoints), then by customer 9 (with three touchpoints), and finally by customer 10 (with only one touchpoint). Thus, investment in a profitable future relationship must be made with customers 1 and 4 (very loyal customers), and 2, 6, and 7 (loyal customers).

According to Belk (2017), Kranzbühler et al. (2019), and Lv et al. (2024), and the touchpoints at each department (Figure 1), the heatmap of each customer can be generated as follows [58,59,60]:

• Very positive customers (colored in red)—Comprising customers 1 and 4 as being the customers with highest shopping intensity, and positive customers (colored in orange)—Comprising customers 2, 6, and 7 with a lower shopping intensity.
• Neutral customers (colored in yellow)—Comprising customers 3, 5, and 8 with a reduced shopping intensity.
• Negative customers (colored in light pink)—Comprising customers 9 and 10, and it shows the lowest shopping value.

Figure 1. The heatmap for each touchpoint (by customer).

Figure 1. The heatmap for each touchpoint (by customer).

By using GeoGebra applications, customer journey mapping was determined (Figure 2) as necessary to model a possible pattern for customers’ shopping actions.

Using modelling (Figure 2), as can be observed, a pattern of the spatial journey mapping was perceived.

According to this pattern, specific for fractal analysis, it can be noticed that each department is visited, and the customers bought different products from different departments according to a certain intensity: department C is the most visited one (by 9 out of 10 customers); A, B, and D by 8 of 10 customers; E and F by 4 of 10 customers; and F by 2 of 10 customers. Thus, the intensity of each department can be determined based on the desire, needs, and preferences of the customers analyzed.

This is called the heatmap of each department, and the customer typology and the visit intensity for each department can be established. The heatmap can be red (for the departments which are most intensely visited), orange (with a lower intensity of visiting), yellow (with a medium intensity of visiting), and pink (with the lowest intensity of visiting) (Figure 3).

According to Lv [60] and Belk [58], the touchpoints can be negative, neutral, positive, and very positive, thus determining the profile of a customer or the intensity of visiting a department in our case.

Based on the above graphical representation, the heatmap for each department analyzed can be established:

• Very positive touchpoints (colored in red)—Represent the intensity of the visits and shopping done in this department, and positive touchpoints (coloured in orange), which have lower intensity but are powerful enough.
• Neutral touchpoints (colored in yellow)—Show that the value obtained from customer shopping is reduced and ask for measures to improve the shopping level.
• Negative touchpoints (colored in light pink)—Show that the value of shopping done at this department is so low that important measures to improve it are needed.

Thus, the following departments, C (design materials), A (electrical), B (construction materials), and D (equipment), are the most visited according to the value registered on the tax receipt.

4.3. Determining Customer Concentration and Mutual Dependency

On one hand, enterprises should build intimate relationships with their clients to accumulate innovative resources. On the other hand, enterprises should reduce CC to avoid operational and financial risks.

$$\mathrm{C}{\mathrm{C}}_5\frac{\left(676+437.55+409.94+351.57+347.27\right)}{3354.38}=0.6625$$

(11)

$$\mathrm{C}\mathrm{C}\mathrm{H}{\mathrm{H}}_5={\left(\frac{676}{3354.38}\right)}^2+{\left(\frac{437.55}{3354.38}\right)}^2+{\left(\frac{409.94}{3354.38}\right)}^2+{\left(\frac{351.57}{3354.38}\right)}^2+{\left(\frac{347.27}{3354.38}\right)}^2=0.0942$$

(12)

As can be seen, the degree of CC is above the average (with a concentration of customers of 66.25%). According to this value, the company does not depend on a single important customer but on more customers, thus ensuring its performance and profitability. CCHH5 is low (9.42%), showing that the company does not depend on major customers, and they have low power over the profitability, innovation, and investment of the company.

According to these calculations, the top five valuable customers (from the point of the purchase value) are customer 9 (first place), customer 6 (second place), customer 2 (third place), customer 7 (fourth place), and customer 4 (fifth place). The CC is not so high, so it is important to attract loyal customers and build a good relationship based on value, trust, and communication.

As we may observe, mutual dependency (

Table 5. Determining the interactions with the most valuable customers and mutual dependency.

Cust	SW (1)	Place After SW	Sij (SWij/Tv) (2)	Cust. Ave. Wage (W)	Total Purch (TP) (90%W) (3)	Pji (SW/TP) (4)	Simetr Mutuality (Sij × Pji) (5)	wij (Sij/Sum of Sij) (6)	MD [wij × (Sij × Pij)] (7)	Place After MD
1	150.96	10	0.045	2500	2250	0.067	0.003	1	0.003	5
2	409.94	3	0.122	3000	2700	0.151	0.018	0.730	0.013	1
3	315.89	6	0.094	3500	3150	0.100	0.009	0.360	0.003	4
4	351.57	5	0.104	4000	3600	0.097	0.010	0.286	0.002	6
5	289.11	7	0.086	3500	3150	0.091	0.007	0.190	0.001	7
6	437.55	2	0.130	2500	2250	0.194	0.025	0.223	0.005	3
7	347.27	4	0.103	4000	3600	0.096	0.009	0.150	0.001	8
8	201.09	8	0.059	4500	4050	0.049	0.002	0.080	0.0002	9
9	676	1	0.201	4000	3600	0.187	0.037	0.212	0.008	2
10	175	9	0.052	3000	2700	0.064	0.003	0.052	0.0001	10
Total (Tv)	3354.38		1

) is between 0 and 1, but not strong enough.

The dependency between the analyzed company and customer 2 (0.013) is the most important one, then customer 9 (0.008), customer 6 (0.0056), customer 3 (0.0034), and customer 1 (0.003). They may be considered loyal customers, and the relationship must be improved. The most reduced dependency is between the company and customer 7 (0.0015064) and customer 5 (0.0015071). They may be considered occasional or transactional relationships, and the investments into these relationships must be reduced.

4.4. Measuring the Correlation Between T, SW, and MD Using Spearman’s Test (r)

By using Spearman’s test (r), the correlation between the number of touchpoints (T), the size of customer value (SW), and the mutual dependency (MD) can be measured (

Table 6. Measuring the correlation between T, SW, and MD using Spearman’s test.

Customer	T	Place for SW	d1 = T-SW	${\mathit{d}}_1^2$	Place for MD	d2 = T-MD	${\mathit{d}}_2^2$	d3 = SW-MD	${\mathit{d}}_3^2$
1	6	10	−4	16	5	1	1	5	25
2	5	3	2	4	1	4	16	2	4
3	4	6	−2	4	4	0	0	2	4
4	6	5	1	1	6	0	0	−1	1
5	4	7	−3	9	7	−3	9	0	0
6	5	2	3	9	3	2	4	−1	1
7	5	4	1	1	8	−3	9	−4	16
8	4	8	−4	16	9	−5	25	−1	1
9	3	1	2	4	2	1	1	0	0
10	1	9	−8	64	10	−9	81	−1	1
T				128			146		53

).

As a result of Spearman’s test, the correlation between T and SW is the following:

$${\mathrm{r}}_{1 }= 1-{\displaystyle \frac{6 \times 128}{10 \times 99}} = 1 - 0.7757 = 0.2243$$

(13)

r₁ = 0.2243 indicates that, between the two factors, there is a weak but positive correlation (22.43%), meaning that many T(s) do not ensure a high value for SW. The point is, if a customer comes, the sales force must persuade them to purchase from the first visit; otherwise, many purchases do not bring great value for the company.

To establish the correlation between T and MD:

$${\mathrm{r}}_{2 }= 1 - {\displaystyle \frac{6 \times 146}{10 \times 99}} = 1 - 0.8848 = 0.1152$$

(14)

r₂ = 0.1152 also indicates that, between the two factors, there is a very weak correlation (11.52%), meaning that many T do not ensure high value for MD between the customer and the company.

To establish the correlation between SW and MD, we calculate the following:

$${\mathrm{r}}_{3 }= 1 - {\displaystyle \frac{6 \times 53}{10 \times 99}} = 1 - 0.3212 = 0.6788$$

(15)

r₃ = 0.6788 indicates that between the SW and MD there is a moderate to strong correlation (67.88%), meaning that a large value for SW may ensure a high value for MD. This means that the more customers purchase from a company, the larger MD will be between the company and the customer.

5. Discussion and Conclusions

This study analyzes customer value to obtain patterns for profitable customers and mutual and sustainable performance, using fractal analysis, tactical indicators, touchpoints, and customer journey in a relational environment.

Studies and interviews demonstrated that between companies and valuable customers there are important mutual benefits [50,82,85,86,100,101] such as interaction, trust, relationship, mutual benefits, involvement, value experience, quality, and reduced risks.

The GeoGebra applications made it possible to establish the way customers moved from one department to another in the company, analyzed based on the heatmaps for the customers. All the touchpoints were direct; however, out of a maximum of 10 touchpoints, only 2 reached 6 touchpoints and 3 reached 5 touchpoints. Thus, only 50% of the customers were attracted by five touchpoints; therefore, the organization must find solutions to improve this issue. Only two customers were in the red zone of positive purchasing intensity, and only one department is in the positive red zone of the heatmap of the customer journey. As a result of comparing the analyzed customers, it is observed that the most valuable customers for the analyzed organization are customers 9, 6, 2, 4, and 7. In analyzing the customers by their number of visits (touchpoints), the customers with the highest visit intensity are noted as 1, 4, 2, 6, and 7. It is established that the less valuable customer (customer 1) visited most (6 touchpoints), and the most valuable customer (customer 9) visited less (2 touchpoints). Thus, any organization needs to carry out fractal analysis: analyze the value of a customer using tactical indicators (mainly SW) and then use the heatmap of each customer to establish the visits (touchpoint). The organization must transform the transactions with the customer with the lowest SW value (customers 3, 5, 8, 10, and 1) into a relationship, as with customers with the highest SW value (customers 9, 6, 2, 4, and 7).

Regarding the intensity of visiting each department, as has been shown, for departments E, G, and F, some improvement measures to create positive or very positive touchpoints are required: attracting and keeping talented sales forces with strong communication, persuasion, information, and presentation skills. Based on Spearman’s test, we established that the number of touchpoints does not influence the SW and MD; there is only a correlation (67.88%) between MD and SW. Therefore, the more the customer purchases at the analyzed company, the higher the mutual dependency is.

The study’s results emphasize that fractal analysis provides a mathematical framework to model non-linear, irregular consumer behaviors and touchpoint complexity that conventional CRM or data analytics fail to capture.

Fractal thinking helped to develop some specific scaling laws across touchpoint paths, referring to the determination of how cost-effective the changes of consumer behavior are with order size or volume, based on last-time attribution during customer journey touchpoints in marketing and customer experience. Using analytical models to predict how changes in the number, type, or sequence of touchpoints will impact a desired organizational outcome, SOW, SW, SCR, CC, or MD were analyzed. This would involve finding a functional relationship between this scale of the touchpoint effort and the organizational performance.

6. Limitations and Future Research Directions

There are some research limitations, such as reduced number of analyzed customers, but we need to have in view that the analysis took place at cell-level as an experiment for future research, future studies on a few companies in the field, or even the use of datamining programs to use large amounts of data in a short time and with reduced costs. However, this could be the start for further research and calculations to analyze customer experience and heatmaps for the department’s monthly or yearly values. Another limitation is the coverage; the used data were only from one organization, but the company is known at the national level and it is among the top three companies from Romania, present in all the counties of the country. This limit could be improved by applying these methods at the supply chain level. Future studies can also expand data across industries, test using machine learning models, or applying the fractal approach longitudinally. Despite these limitations, this study holds many important contributions to enriching knowledge and the literature in the relationship marketing field.

By understanding the value of a customer based on modelling and touchpoints present in a customer journey, the company can discover possible patterns to easily analyze the customer’s behaviors and movement and build relationships with its valuable customers according to win-win principles. Companies invest in relationships, not in transactions, so by knowing the value of a profitable customer and their journey across their departments the customer’s experience could be improved and loyalty and satisfaction could be obtained.

The study has important theoretical and practical implications for customers, managers, departments/stores, and companies, which are presented below.

6.1. Theoretical Implications

This research contributes to the existing literature, confirming that touchpoint intensity and customer journey mapping are important tools for value creation. Customer experiences analysis may help companies to understand the needs, desires, and preferences of a customer, leading to increased performance for both involved parties. Customer journey mapping is a tool that helps organizations to know the insights of its customers: behaviours, believes, feelings, desire to communicate and relate, needs, desires or preferences. Touchpoints are another important tool used to help customers inform organizations about their needs and desires and the organizations to know how they can satisfy their needs on another level. Fractal analysis could help companies to determine possible patterns of customer behaviour; thus, value creation will be a win-win situation based on trust, relationship, help, information, and loyalty. Also, this study confirmed the importance of organizational performance in the relationship between characteristics of a touchpoint and the value of a customer.

6.2. Practical Implications

These findings encourage organizations to focus on improving the performance of a touchpoint using modelling, thus making it easier to maximize the value perceived by customers.

Moreover, this study offers the opportunity for companies to detect which customer is more valuable and invest in their relationship and which department lacks a relationship with the customer, thus investing in its employees and their training. Patterns determined using customer mapping and touchpoint intensity may help organizations to determine, with reduced costs, the value of a customer, possible choices of customers, and offer real benefits to profitable customers to increase their loyalty and satisfaction.

This study will allow the management team to gain insights into customer value, improve customers’ experience and customer concentration, and to develop heatmaps for the analyzed departments for mutual relationships and performance. From a practical perspective, managers can use these patterns to adjust their strategies to maintain profitable customers, to maintain healthy relationships, invest in developing and maintaining an effective touchpoint based on speed optimization, develop new skills, or determine the cost of a touchpoint using fractal thinking, which helped to develop some specific scaling laws across touchpoint paths. The scale used will bring closer the marketing operations and customer efforts across their possible journeys and touchpoints without compromising the quality of the tactical indicators used. So, using automation and data mining will help companies to offer personalized experiences to a larger audience or develop more general principles to determine customer behavior across different paths or channels. Thus, the efficiency of customer interactions will change the volume, complexity, or personalization of these touchpoints, increasing within the non-linear customer journey.

6.3. Practical Implications for Employee-Customer Interaction

At the employee–customer interaction level, value creation will have resulted in increased offerings of personalized products, communication and experiences, satisfaction, loyalty, information sharing, improved mutual benefits, enhanced quality of products and services, reduced prices, diverse offerings, constant interactions and relationships, amiability, empathy, and hedonic benefits, adhering to the principle of happy customers, happy employees and enhancing their overall experience, which leads to increased satisfaction and loyalty. Fractal thinking will determine new patterns for customer behavior and will optimize these interactions through personalized and supportive communication, improve the customer’s journey, solve problems efficiently, lead to more satisfied customers, build stronger and lasting relationships with the brand and more satisfying journeys, make customers feel valued, create interactions based on trust, provide more improved services, and obtain more engaged customers through loyalty programs and better experiences.

In conclusion, this study emphasizes the significance of the link between an appropriate touchpoint and value for company and customers, providing valuable theoretical contributions and encouraging practical applications that can improve performance at the cell and organizational level based on fractal analysis.