Line Replacement Fractals

draw a fractal based on iterated line replacement

Koch snowflake

Minkowski sausage

Cesaro fractal

Shape Replacement Fractals

draw fractals based on replacement of shapes

Sierpinski gasket

draw fractals by repeatedly adding smaller figures

Pythagoras tree

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)

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

Mandelbrot & Julia Sets

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

Fractals in 3D

draw the Sierpinski tetrahedron

Sierpinski tetrahedron

draw the Menger sponge

Menger sponge

Other Fractals

plot a curlicue fractal

curlicue fractal