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 ,<i>d</i>,:

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