No research has been conducted on the emotional impact of geometric patterns so far, so surveying them was one of the key tasks of this research. To understand this aspect of human behaviour, first of all, focus group interviews, and after that, questionnaire techniques were used.
3.1. Focus Group Interview
The focus group technique is a type of qualitative research, where the participants are engaged in a guided conversation on a topic. The key question of this examination was the reactions caused by certain patterns. In this research stage, two focus groups were involved, and the results of these sessions were used as the basis for the survey.
The patterns were printed in 3D to help its evaluation. These prototypes allowed the patterns to be presented much more easily and the interviewees could discuss it effectively and creatively.
3.1.1. Creating Patterns
Patterns are basically created by the (re-) arrangement and transformation (for instance, multiplications, rotation) of basic geometric elements. In this project, the patterns were deliberately chosen to elicit sharply different impressions of different shapes. A total of six patterns were created, each of which will be presented along with the three- phases of their development (
Figure 7).
In patterns 2, 5 and 6, the base of the patterns was chosen from among the mood lines of Simonds. Different geometrical transformations were made to these patterns in order to design the final pattern. In patterns 1, 3, and 4, the above-mentioned mood lines can be recognized in the general appearance of each pattern. In order to create the patterns, different topologies and structures were applied. During the background research, the process of seeing, the methods for creating feelings, and the details of achieving a given effect were examined. This research suggested the idea of analysing cognition through optical illusions. In addition to that, examining confusing phenomena is both interesting and entertaining, and these aspects proved to be a vital component of the efficient analysis of the connections between design and psychology.
First Pattern
There are three main types of optical illusions have: optical illusions in the literal sense, physiological illusions, and cognitive illusions. Within cognitive illusions, the area of depth and motion detection was studied, and the essence of this is that the viewers will see an image in three dimensions even if the light is projected on the retina in two dimensions [
33]. For the ridge pattern, undulation was chosen which symbolizes rhythm. Related expressions are smooth, swelling, and sliding (
Figure 5).
Several examples demonstrate the theory that the alternation of bigger and smaller pattern groups evokes the notion of rhythm. The base for the pattern is made of ellipses, because psychological studies have shown that people find round, rounded, or curved-cornered polygons more sympathetic than rectangular geometry. The basic ellipse, the base for the regular shape, and the final pattern can be seen in
Figure 8.
The basic elements of the pattern were repeated several times, keeping the same distances and then it was reproduced in perpendicular directions.
Second Pattern
Related expressions for the basic geometry are logical, planned, and orderly (
Figure 5). Based on the basic geometry the base for the repetitive structure was created (
Figure 9).
Third Pattern
Hermann Ebbinghaus, an experimental psychologist who studied learning and memory patterns, inspired the third pattern. He himself created the illusion named after him. Circles were used for the repeating basic elements [
34].
In the Ebbinghaus illusion, the phenomenon of relative size perception can be examined. The two internal circles are of the same size, but most people see the first (the circle on the left) as larger than the second one (on the right). The reason is that smaller circles surround the circle on the left while large circles surround the circle on the right (
Figure 10).
Fourth Pattern
This is an example of optical art, which influences the human feeling of space and spatial approach. The laws of geometry and mathematics affect this. This genre, known as Op-Art, uses basic geometric shapes and distributes them according to a pre-conceived plan. Squares were used and arranged in a variable density perspective, starting from the middle of the image. The dimensions of the rectangles change gradually and symmetrically (
Figure 11).
Fifth Pattern
The fifth pattern (
Figure 12) is characterized by a spiral that has connotations of concentration and focus. However, this pattern has a different appearance because this is the only pattern that is asymmetrical. This element of the research was a chance to find out whether people see something beautiful only if it is symmetric and proportional (as other studies have claimed [
35]). Furthermore, it was suggested that the asymmetry could cause creativity and interest.
Sixth Pattern
Related expressions for the basic geometry of this pattern are curvilinear, tender, soft, pleasant, feminine, and beautiful (
Figure 5). Based on the basic geometry, a base for the repetitive structure was created (
Figure 13).
3.1.2. The Interview Structure
At the beginning of the interview, the members of the focus group provided demographic data and were asked a few basic questions concerning their age, gender, educational attainment, occupation, favourite colour, favourite product, and basic sentiment.
After gathering this information, some technical issues were taken into consideration, for example, the reason for this study, time management, confidentiality and voice recording.
Before the main task, a brainstorming assignment helped the members to understand what exactly the issue was. The main task was based on design team work, in which the groups completed a task involving six questions about the pattern. These questions focused on the related words, products, patterns, spaces, colours, touch and emotions that they felt. Finally, the evaluation and collation of information was carried out.
In total, 22 people (10 women and 12 men) participated in the interviews. The subjects’ age ranged from 22 to 36 (M = 26 years, SD = 3.53). They were predominantly university graduates or still students. In terms of their occupation, almost all were in employment, in positions such as HR manager, graphic artist, and financial analyst. They mainly worked in the technical and financial fields, and some also had experience in product design. The most common favourite colours given were purple, green, and blue. The respondents’ favourite products include mainly computer equipment, entertainment products, food, and electronics products. Their mood was mostly positive.
3.1.3. Results of Focus Groups Interviews
The keywords about each of the patterns are summarised in
Table 2. The results about the patterns are described in detail separately below the table.
First pattern: The feelings and effects indicated about this pattern correspond well with the depth and movement illusions it was supposed to create, while the fluctuating feeling—indicated by the rhythmic spread of the pattern—was also mentioned multiple times. The elliptical base of the pattern produced a pleasant and calming effect—as had been planned in advance. The fluctuating feeling led to a number of associations being made with water—waterfall, water drop, foam etc. Areas connected to the patterns were all based on its character, so the porosity was cited as a function in many cases. Considering the possible colours, the brighter shades were dominant.
Second pattern: The base-geometry was meant to evoke a logical, planned, arranged feeling, although manipulating it allowed a significantly different effect to be achieved. Many of the participants associated it with claustrophobic or secure feelings, or mentioned similar products in connection with it, like fences, bars, and rails. Given the obvious similarities with the cross symbol, churches or even cemeteries were also frequently mentioned. As for colours, various shades of brown were suggested the most often.
Third pattern: The illusion of circles was not mentioned, only the shape of a flower or the sun—both consisting of the base circles—and their effects. The feelings it evoked were all positive ones, such as calmness, home and nostalgia. The areas and products which respondents suggested were also mainly connected to one’s home and household, like goods based on paper and textile. Bright and “happy” colours were the most frequently mentioned.
Fourth pattern: Feelings associated with space and mathematics were elicited by the base of the pattern, although the areas of application suggested were typically more “hectic” areas such as show business and sport. Interestingly, the colours which respondents associated with this pattern were all strongly contrasting, such as black and white.
Fifth pattern: The asymmetric helix-shape was meant to be an exception among the other symmetric patterns. It was clearly the most creative example and also the one that provided the most information. It even caused minor arguments, because multiple teams wanted to analyse this pattern. The words most frequently used about it by the respondents were movement, dizziness, harmony, wind, universe and variants on these themes. Of the most common words related to feelings included brilliant, spiritual and developing. The participants mentioned many different areas, mainly concerning contrast and bright colours.
Sixth pattern: Given its soft, pleasant, feminine base-geometry, the sixth pattern delivered the expected effect in most cases—the participants would mostly use it in decoration and architecture—although, it was also the most controversial pattern. Most of participants considered it to be elegant and artistic. However, a significant portion of the participants found it unpleasant and boring. With regard to colours, mainly very dark or very bright shades were mentioned.
3.2. Questionnaire
Quantitative research techniques include the survey, which should contain major questions directly related to the research topic, along with additional questions on related subjects, because these can obtain information and identify possible biases.
The questionnaires were based on the three main phases of pattern preparation. The questionnaire was divided into three parts. The questions in the first part concerned the basic geometry, e.g., square, circle, etc., while in the second part they focussed on the geometry of the repeating unit, and in the third part the finished pattern was the subject of the questions. Six types of questionnaires were created.
In order to incorporate the results of the interviews into the questionnaire, the evoked feelings, characteristics, colours, and areas of application most frequently mentioned for each pattern during the interviews were collected. In total, five characteristics (feelings, emotions, moods), two colours, and five application areas were asked about in the survey questions (
Figure 14). The participants were required to sort the areas of application of the patterns, while their opinions about characteristics and colours were elicited separately. For example, for Pattern 1, the first question was, “How calming is the geometry/pattern?” The answers could be: “Not at all”, “Not really”, “Mostly” and “Completely”.
A total of 534 people (108 women, 426 men) participated in the survey. The participants were primarily students of the Faculty of Mechanical Engineering. A survey of the basic preferences of the respondents revealed that blue was the most popular colour when asked about their favourite colours, followed by green, then black and red, and finally yellowish, brownish, and white. Among their favourite products, technical products are the most popular, followed by excise goods and food. Among the technical products, phones, laptops, and other electronic items predominated.
The subjects’ responses (“Not at all”, “Not really”, “Mostly” and “Completely”) were quantified. Similarly to the method used for the ergonomic evaluation of products (importance–satisfaction chart) [
36], the values were weighted. The following values were added to the answers, since on a scale from “Not at all” and “Completely”, this is an easy division, and it is also straightforward to represent:
Not at all—0 point
Not really—1 point
Mostly—2 points
Completely—3 points
The subsequent calculation aims to represent the results in a coordinate system, where X, Y, and Z-axes denote the characteristics of the three subsamples about one pattern. The values of the axes can be interpreted up to a maximum of 3, where 3 denotes the terms “Completely” and 0 denotes the terms “Not at all”.
The coordinates are defined as follows:
Weighted value: The sum of the products of the answers and the corresponding points. In the example of
Table 3:
Average = coordinate: Dividing the weighted value by the number of respondents produces the average, which will denote the coordinate point of the given axis. In the example in
Table 3:
Based on the same idea, it will be possible to add a coordinate to each question. In these, three answers to the same question define a node (X, Y, Z) since pattern creation involves three phases.
The X coordinate belongs to phase 1 of the pattern creation, to the basic geometry, the Y coordinate to phase 2, which is mostly the repeating element, and the Z coordinate belongs to the finished pattern (
Table 4).
Based on the tables above (
Table 3 and
Table 4), in the first pattern, the answer to the question, “How calming is the pattern?” node (1.4,1.1,1.2) can be associated (
Figure 15). A pattern has seven nodes.
If the steps described above are applied to all six patterns, the resulting coordinates can be summarized in a node table. Based on the data, several conclusions can be drawn, but one of the most interesting is obtained when examining the highest values.
Table 5 shows the part of the summarized node table relating to the third pattern. The numbers in bold—and their columns—indicate which sub-pattern the responders consider the property (Column 1) to be most characteristic of.
Based on the results, it can be assumed that the characteristics can be derived from the step (sub-pattern or pattern) to which the highest values are associated. This means that when, for example, participants in a focus group interview found the third pattern calming, they did not know that the reason for this was that the pattern was made up of circles. They merely felt that way. However, it can be seen that when examined separately, the circle represents the most calming feeling, and although the calming effect decreased as the pattern was altered, it was still felt in the end result. Hence, the characteristics that had the highest values in the first column of the values, i.e., in the first phase of pattern generation (basic geometry), are derived from that geometry. In each case, the evoked feelings above can be seen to diminish during the process of transformation but they remain present throughout. For the phases in the second, and especially the third column, it can be concluded that the way the pattern is made gives it the property.
For example, observing the undulating property of the first pattern (
Table 6), it is clear that since the pattern creation was aimed at portraying the undulating character, the values also increase during the pattern development process. Based on these, it can be postulated that the properties of a pattern (except for colours) can come from two sources: on the one hand from the characteristics of the basic geometry, and on the other hand from the way the pattern is made.
Visually displaying the points can further help in drawing conclusions. For more straightforward transparency, the first pattern points are shown in a 2D view, i.e., by showing two axes (
Figure 16). The points located on the 1 slope of line starting from point (0;0) would be the ones for which the average opinion and feeling of the survey participants would not have changed with the modification of the pattern. The environment of this line is characterized by a slight change in the respondents’ opinion regarding the modification of the pattern, more precisely, areas 2 and 3 of the parts of the diagram divided towards 4, cover it. However, in this way, the factors that may be most influenced by modifying a given pattern can also be distinguished. These factors are included in the questions for nodes in areas 1 and 4, marked with a uniform colour scheme. In the diagram, the points on the boundary lines and on areas 1 and 4 were also marked in red. The conclusions about the examination of the diagrams are presented in the next section.