# Application of the Fractal Dimension Calculation Technique to Determine the Shape of Selected Monchepluton Intrusion Crystals (NE Fennoscandia)

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{1}and x

_{2}correspond to the number of passes of the individual squares x

_{1}, and x

_{2}of the contour of the shape, with d

_{1}, and d

_{2}of their respective side lengths.

## 3. Results

#### 3.1. Monchepluton Petrography

#### 3.2. Rock-Forming Minerals Characteristic

#### 3.3. Fractal Analysis Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematic sketch of the Monchepluton intrusion (according to Mitrofanov and Smolkin [25], simplified by the author) with the location of the tested samples. Legend: (1) dunite, chromitite; (2) harzburgite; (3) other peridotites; (4) orthopyroxenite; (5) norite, olivine norite; (6) gabbronorite; (7) gabbro; (8) anorthosite; (9) sulfide ore mineralization; (10) samples localization; (11) rocks of the Monchetudra massif; (12) rocks of the Imandra–Varzuga Belt; (13) rocks of the Kola Series. The red-orange star in the map inset, symbolizes the location of the intrusion on the Scandinavian background.

**Figure 2.**Example of counting crystal boundary contour process: image taken from the microscope camera (

**A**), marking the field of the study area (

**B**), sharpening the boundaries of the crystals (

**C**), identifying and selecting the mineral crystals for analysis (

**D**), applying a grid for counts (

**E**), determining those grid areas that form the boundaries of the selected crystals (

**F**).

**Figure 3.**Examples of typical rocks from Moncheplutonu. (

**A**) Dunite. (

**B**) Harzburgite. (

**C**) Orthopyroxenite. (

**D**) Gabbronorite. Abbreviations: opx -orthopyroxene, cpx—clinopyroxene, ol—olivine, chr—chromite, pl—plagioclase.

**Figure 4.**Different shapes of olivine. (

**A**–

**C**) Orthopyroxene. (

**D**–

**F**) Clinopyroxene. (

**G**–

**I**) Plagioclase. (

**J**–

**L**) Olivine co-occurring in dunite. (

**A**) Euhedral olivine crystal. (

**B**) Euhedral olivine crystal in harzburgite. (

**C**) Melted olivine in myllonitized peridotite. (

**D**) Orthopyroxene in orthopyroxenite. (

**E**) Orthopyroxene in harzburgite. (

**F**) Corroded orthopyroxene in norite. (

**G**) Clinopyroxene in orthopyroxenite. (

**H**) Clinopyroxene in norite. (

**I**) Clinopyroxene in saussuritized gabbro. (

**J**) Plagioclase in orthopyroxenite. (

**K**) Plagioclase in norite (

**L**) Plagioclase in plagioharzburgite. Abbreviations: opx—orthopyroxene, cpx—clinopyroxene, ol—olivine, chr—chromite, pl—plagioclase.

**Figure 5.**Maps of fractal dimension distribution for (

**A**) olivines, (

**B**) plagioclases, (

**C**) orthopyroxenes, and (

**D**) clinopyroxenes. Abbreviations: Tr—Traviannaya; Ku—Kumuzhia; Ni—Nittis; DB—Dunite Block; So—Sopcha; Ny—Nyud; Po—Poaz. The scale in figures represents values from 0 to more than 130%, indicating the manner of complexity of the crystal boundary. A value of 100% is taken to be euhedral in shape; lower values indicate more spherical, simple forms, while higher values indicate strongly frayed crystals with an elaborate boundary. A value of 0% means there is no crystal in the rock sample under study.

**Figure 6.**Map showing the % sum of the fractal ratio for olivine, orthopyroxene, clinopyroxene, and plagioclase in Monchepluton. Abbreviations: Tr—Traviannaya; Ku—Kumuzhia; Ni—Nittis; DB—Dunite Block; So—Sopcha; Ny—Nyud; Po—Poaz.

**Figure 7.**Correlation of the fractal dimension for couples: olivine—orthopyroxene (

**A**), olivine—clinopyroxenes (

**B**), olivine—plagioclase (

**C**), orthopyroxene—plagioclase (

**D**), orthopyroxene—clinopyroxenes (

**E**), orthopyroxene—plagioclase (

**F**). Abbreviations: ol—olivine; opx—orthopyroxene; cpx—clinopyroxene; pl—plagioclase.

Sample | Massif | Latitude | Longitude | Sample | Massif | Latitude | Longitude |
---|---|---|---|---|---|---|---|

46MON17 | Dunite Block | 67°53′57.4″ N | 32°45′59.0″ E | 32MON19 | Sopcha N | 67°53′36.30″ N | 32°48′53.32″ E |

02MON19 | Dunite Block | 67°53′49.09″ N | 32°44′57.01″ E | 39MON19 | Sopcha N | 67°53′36.31″ N | 32°48′53.35″ E |

56MON17 | Dunite Block | 67°53′57.4″ N | 32°45′59.0″ E | 40MON19 | Sopcha N | 67°53′36.32″ N | 32°48′53.38″ E |

67MON17 | Traviannaya | 67°56′33.0″ N | 32°49′03.3″ E | 38MON16 | Sopcha W | 67°53′29.7″ N | 32°49′59.1″ E |

01MON19 | Traviannaya | 67°56′38.15″ N | 32°48′40.18″E | 39MON16 | Sopcha W | 67°53′33.7″ N | 32°50′03.4″ E |

07MON18 | Traviannaya | 67°56′38.2″ N | 32°48′40.2″ E | 42MON16 | Sopcha W | 67°53′40.5″ N | 32°50′11.0″ E |

84MON17 | Traviannaya | 67°56′32.4″ N | 32°48′08.3″ E | 43MON16 | Sopcha W | 67°53′40.52″ N | 32°50′11.05″ E |

03MON19 | Kumuzhia | 67°55′44.3″ N | 32°48′03.9″ E | 44MON16 | Sopcha W | 67°53′49.5″ N | 32°49′54.6″ E |

04MON19 | Kumuzhia | 67°55′45,55″ N | 32°47′29.51″ E | 45MON16 | Sopcha W | 67°53′49.51″ N | 32°49′54.63″ E |

05MON19 | Kumuzhia | 67°55′45,54″ N | 32°47′29.53″ E | 08MON17 | Nyud | 67°53′11.3″ N | 32°53′57.3″ E |

07MON19 | Kumuzhia | 67°55′50.88″ N | 32°47′26.16″ E | 09MON17 | Nyud | 67°53′11.3″ N | 32°53′57.3″ E |

18MON19 | Nittis | 67°55′05.48″ N | 32°45′32.88″ E | 14MON17 | Nyud | 67°53′29.15″ N | 32°54′48.02″ E |

29MON17 | Sopcha E | 67°53′09.2″ N | 32°52′48.6″ E | 15MON17 | Nyud | 67°53′29.2″ N | 32°54′48.1″ E |

30MON17 | Sopcha E | 67°53′09.2″ N | 32°52′48.6″ E | 16MON17 | Nyud | 67°53′31.7″ N | 32°54′55.7″ E |

31MON17 | Sopcha E | 67°53′09.24″ N | 32°52′48.6″ E | 20MON17 | Nyud | 67°53′31.75″ N | 32°54′55.77″ E |

32MON17 | Sopcha E | 67°53′09.25″ N | 32°52′48.6″ E | 22MON17 | Nyud | 67°53′38.3″ N | 32°55′21.1″ E |

34MON17 | Sopcha E | 67°53′23.3″ N | 32°52′05.1″ E | 24MON17 | Nyud | 67°53′38.2″ N | 32°55′22.4″ E |

38MON17 | Sopcha E | 67°53′41.7″ N | 32°51′17.2″ E | 58MON17 | Poaz | 67°54′58.5″ N | 32°58′36.0″ E |

31MON19 | Sopcha N | 67°53′36.30″ N | 32°48′53.30″ E | 61MON17 | Poaz | 67°54′56.5″ N | 32°58′20.5″ E |

Sample | Fractal Analysis Results | Massif | Sample | Fractal Analysis Results | Massif | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|

ol | opx | cpx | pl | ol | opx | cpx | pl | ||||

46MON17 | 1.81 | 1.75 | 1.43 | Dunite Block | 40MON19 | 1.61 | Sopcha N | ||||

52MON17 | 1.76 | 1.36 | Dunite Block | 38MON16 | 1.39 | 1.71 | 1.63 | Sopcha W | |||

02MON19 | 1.53 | 1.75 | 1.42 | 1.72 | Dunite Block | 39MON16 | 1.74 | 0.87 | Sopcha W | ||

03MON19 | 1.63 | 1.70 | 1.01 | Kumuzhia | 42MON16 | 1.71 | 1.77 | 1.54 | 1.10 | Sopcha W | |

04MON19 | 1.69 | 1.81 | 1.33 | Kumuzhia | 43MON16 | 1.72 | 1.26 | Sopcha W | |||

05MON19 | 1.67 | 1.64 | Kumuzhia | 44MON16 | 1.07 | 1.80 | 1.14 | Sopcha W | |||

07MON19 | 1.75 | 1.73 | 1.25 | 1.00 | Kumuzhia | 45MON16 | 1.72 | 1.69 | Sopcha W | ||

18MON19 | 1.49 | 1.68 | 1.19 | 1.39 | Nittis | 08MON17 | 1.79 | 1.33 | Nyud | ||

58MON17 | 1.73 | 1.29 | 1.74 | Poaz | 09MON17 | 1.69 | 1.51 | Nyud | |||

61MON17 | 1.77 | Poaz | 14MON17 | 1.58 | 1.69 | 1.84 | 1.58 | Nyud | |||

29MON17 | 1.50 | 1.75 | Sopcha E | 15MON17 | 1.65 | 1.38 | 1.50 | Nyud | |||

31MON17 | 1.76 | 1.48 | 1.43 | Sopcha E | 16MON17 | 1.76 | Nyud | ||||

32MON17 | 1.67 | 1.35 | Sopcha E | 20MON17 | 1.46 | 1.77 | 1.54 | 1.69 | Nyud | ||

34MON17 | 1.54 | 1.72 | 1.60 | Sopcha E | 22MON17 | 1.73 | 1.39 | 1.78 | Nyud | ||

38MON17 | 1.61 | 1.68 | 1.15 | Sopcha E | 24MON17 | 1.64 | 1.70 | 1.32 | Nyud | ||

30MON17 | 1.74 | 1.65 | 1.30 | Sopcha N | 01MON19 | 1.73 | 1.76 | 1.74 | Traviannaya | ||

31MON19 | 1.68 | 1.68 | Sopcha N | 07MON18 | 1.62 | 1.75 | 1.40 | Traviannaya | |||

32MON19 | 1.75 | 1.37 | Sopcha N | 67MON17 | 1.75 | 1.27 | Traviannaya | ||||

39MON19 | 1.72 | Sopcha N | 84MON17 | 1.47 | 1.69 | 1.57 | 1.63 | Traviannaya |

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**MDPI and ACS Style**

Huber, M.; Stępniewska, K.
Application of the Fractal Dimension Calculation Technique to Determine the Shape of Selected Monchepluton Intrusion Crystals (NE Fennoscandia). *Minerals* **2021**, *11*, 1140.
https://doi.org/10.3390/min11101140

**AMA Style**

Huber M, Stępniewska K.
Application of the Fractal Dimension Calculation Technique to Determine the Shape of Selected Monchepluton Intrusion Crystals (NE Fennoscandia). *Minerals*. 2021; 11(10):1140.
https://doi.org/10.3390/min11101140

**Chicago/Turabian Style**

Huber, Miłosz, and Klaudia Stępniewska.
2021. "Application of the Fractal Dimension Calculation Technique to Determine the Shape of Selected Monchepluton Intrusion Crystals (NE Fennoscandia)" *Minerals* 11, no. 10: 1140.
https://doi.org/10.3390/min11101140