Mathematics
# Fractals

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Line Replacement Fractals

draw a fractal based on iterated line replacement

Koch snowflake
Minkowski sausage
Cesaro fractal
draw fractals based on replacement of shapes

Sierpinski gasket
draw fractals by repeatedly adding smaller figures

Pythagoras tree
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Nowhere Differentiable Functions

plot an approximation to a nowhere-differentiable function

blancmange function, n=8
evaluate a nowhere-differentiable function at a point

Takagi function(123/467)
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Space-filling Curves

plot an approximation to a space filling curve

Peano curve
Hilbert-2 curve
specify the number of iterations to use

Hilbert curve, n=5
plot a Julia set

Julia set -0.40+0.65i
plot the Mandelbrot set

Mandelbrot set
plot the multibrot set of exponent d

multibrot set, d=6
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Fractals in 3D

draw the Sierpinski tetrahedron

Sierpinski tetrahedron
draw the Menger sponge

Menger sponge
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Other Fractals

plot a curlicue fractal

curlicue fractal