Box Fractal

Author

Eric W. Weisstein
August 31, 2016

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Fractals/BoxFractal.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/BoxFractal.html.

©2016 Wolfram Research, Inc. except for portions noted otherwise

Graphic

V5

Show[GraphicsArray[Block[{$DisplayFunction=Identity},ArrayPlot/@fractal[{0,4}]]],ImageSize->500]

ArrayPlot[fractal[5],PixelConstrained->True]

V6

GraphicsRow[ArrayPlot/@BoxFractal/@Range[0,4]]

V11

rules={
1->{{1,0,1},{0,1,0},{1,0,1}},
0->ConstantArray[0,{3,3}]
};

RulePlot[SubstitutionSystem[rules]]

its=SubstitutionSystem[rules,{{1}},5];

GraphicsGrid[Partition[ArrayPlot/@its,3]]

Dimension

Count[#,1,2]&/@its

FindSequenceFunction[%,n+1]

Table[5^n,{n,0,7}]

-Limit[((Log[(5^n)])/(Log[(3^(-n))])),n->∞]

N[%]

L-System

Show[GraphicsArray[Table[LSystemPlot[{"F"->"F-F+F+F-F"},"F-F-F-F",n,90,1,{0,0},{1,0},10^5],{n,0,3}]],ImageSize->500]