A fractal is a collection of geometric patterns found both in nature and in the form of visualizations in mathematical models, where the pattern is repeated on a smaller scale. Fractal geometry not only characterizes geometric images, but also reflects the processes of formation and evolution. In simple terms, fractal geometry is an irregular geometric shape that has the property of self-similarity at different scales. Fractals can be built using one of the techniques, namely the iteration technique. One of the fundamental requirements for successful exploration and evaluation of mineral deposits is the preparation of a description of the spatial distribution of mineral deposits. The geological processes in the formation of ore deposits can be determined by combining information about the distribution of ore deposits with geological data. The purpose of writing this article is to find out the application of fractals by showing the theorem of fractal geometry proved to be a useful concept for solving problems in geology and the mining industry. The results show that the concept of fractals has proven to be a very useful way of describing naturally occurring dimensional statistics. The spatial distribution of mineral deposits from fractal dimension calculations provides fundamental implications for exploration. The degree of exploration of an area can be assessed by comparing the observed fractal dimensions with known values. The importance of the application of fractal analysis in geology, useful in the geometric determination of mineral deposits, particularly in the study of fracture parameters, and especially in dealing with the assessment of the variability of geotechnical parameters for the purpose of further planning the direction of mining operations.

1.
B.B.
Mandelbrot
.
The Fractal Geometry of Nature.
New York
;
1983
.
2.
Burton
,
David
M.
The history of Mathematic an introduction
Seventh Edition.
2017
;
3.
Sekawati
L.
Technique for Describing Natural Shapes and Images Based on Fractal Dimensions.
2012
;
4.
Sahid
.
Self-Resembling Curve Fractals.
J Educator Mat FMIPA Yogyakarta State University
.
2017
;
5.
Turcotte
DL
.
Fractals, chaos, self-organized criticality and tectonics.
Terra
Nov.
1992
;
6.
Axelsson
C.
The implication of fractal dimension in hydrogeology and rock mechanics.
Version 1.1.
1992
;(February).
7.
Wang
B
,
Lea
C
,
Y.
Js
. Fractal Surfaces: Measurement and Applications in The Earth Sciences.
Earth Sciences Division
,
Lawrence Berkeley Laboratory
,
Berkeley
, Ca 94706;
1993
.
8.
Seidel
JP
,
Haberfield
C.
The use of fractal geometry in a joint shear model.
Mechanics of Jointed and Faulted Rock. A. A. Balkema.
Rotterdam
;
1995
.
529
534
p.
9.
Kulatilake
PHSW
,
Shou
G
,
Huang
TH
,
Morgan
R.
New Peak Shear Strength Criteria for Anisotropic Rock Joints
.
Int J Rock Mech Min Sci Geomech.
1995
;
32
:
673
697
.
10.
Kusumayudha
SB
,
Zen
MT
,
Notosisyono
S GR
.
Fractal Analysis of the Oyo River flow in the Southern Mountains of Central Java, Lithological Control and Geological Structure
.
J Teknol Miner.
1997
;
IV
(
2
):
71
86
.
11.
Carlson
C.
Spatial Distribution of Ore Deposits
.
Geology.
1991
;
19
:
111
114
.
12.
Machulla
J.N.
& G.
Protolytic Weathering of Montmorillonite
,
Described by Its Effective Surface Fractal Dimension.
1994
;
13.
Blenkinsop
T.G.
Applications of fractal geometry to mineral exploration
.
SEG 2004 Predict Miner Discov Under Cover.
2004
;
14.
Kusumayudha
SB
.
Hydrogeological conceptual model of the Kulonprogo dome based on fractal geometry mapping and analysis
. In:
Proccedings PIT IAGI Lombok, The 39th IAGI Annual Convention and Exhibition.
2010
.
15.
Panasiuk
A.
Analysis of fractal characteristics of mining and geological parameters of minerals
.
2016
;(
10
):
42
5
.
16.
Maanijou
M
,
Daneshvar
N
,
Alipoor
R
,
Azizi
H.
Spatial Analysis on Gold Mineralization in Southwest Saqqez Using Point Pattern, Fry and Fractal Analyses
.
Geotectonics.
2020
;
54
(
4
):
589
604
.
17.
Brian H.
Kaye
.
Fractal Geometry and the Mining Industry, a Review.
1994
;
18.
Xie
H.
Fractal in Rock Mechanics. Geomechanics Research Series 1,
China University of Mining and Technology, Xuzhou and International Centre for Material Physics
,
Academia Sinica
,
Shenyang
.;
1993
.
19.
Turcotte
DL
.
A fractal approach to the relationship between Ore Grade and Tonnage
.
Econ Geol.
1986
;
81
:
1528
32
.
20.
Lange
MA
,
Ahrens
TJ
,
Boslough
,
M B.
Impact cratering and spall failure of gabbro
.
Icarus.
1984
;
58
:
383
95
.
21.
Hartman
WK
.
Terrestrial, lunar and interplanetary rock fragmentation
.
Icarus.
1969
;
10
:
201
13
.
22.
Bennet
JG
.
Broken coal
.
J Ins Fuel.
1936
;
10
:
22
39
.
23.
Fujiwara
A.
Destruction of basaltic bodies by heigh-velocity impact
.
Icarus.
1977
;
31
:
277
88
.
24.
Pal
SK
,
Chakravarty
D.
Rock-mass Characterization using Fractals
.
2015
;(January).
25.
Mo-Xiao
L
,
Guang
Z
,
Jing-Xi
C.
Research on the surface fractal characteristic of the rock with rockburst proneness
.
Indones J Electr Eng Comput Sci.
2016
;
1
(
2
):
349
53
.
26.
Gao M
zhong
,
Zhang J
guo
,
Li S
wei
,
Wang
M
,
Wang Y
wei
,
Cui P
fei
.
Calculating changes in fractal dimension of surface cracks to quantify how the dynamic loading rate affects rock failure in deep mining
.
J Cent South Univ.
2020
;
27
(
10
):
3013
24
.
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