Fractals

Lindenmayer Systems

X → F+[[X]-X]-F[-FX]+X

Fractal Plant

variables : X F
constants : + − [ ]
start : X
rules : (X → F+[[X]-X]-F[-FX]+X), (F → FF)
angle : 30°
Fractal Plant (7 iterations)

Dragon Fractal

variables : X Y
constants : F + −
start : FX
rules : (X → X+YF+), (Y → −FX−Y)
angle : 90°
Dragon Fractal (14 iterations)

Fractal Curve Tree

constants : F + −
start : F
rules : F → FF-[-F+F+F]+[+F-F-F]
angle : 22.5°
Fractal Curve Tree (5 iterations)

Closed Fractal

variables : X Y
constants : F + −
start : XYXYXYX+XYXYXYX+XYXYXYX+XYXYXYX
rules : (F → ), (X → FX+FX+FXFY-FY-) , (Y → +FX+FXFY-FY-FY)
angle : 90°
Closed Fractal (4 iterations)

Penrose Tiling

Penrose tiling v1 ( 4 iterations )
Penrose tiling v2 ( 9 iterations )

Mandlebrot Sets

z(0) = z,    z(n+1) = z(n)*z(n) + z,    n=0,1,2, ...   
Mandlebrot Set

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