Gallery of Randomly Generated IFS

Created by Paul Bourke
March 1998

Colour examples

The following images are a selection from an infinite set of Random Iterated Function Systems (IFS) of the form

xn+1 = a xn + b yn + c

yn+1 = d xn + e yn + f

The image is formed by drawing a point at each iteration at the position (xi,yi).

For the mapping to contractive the following must all be true.

a2 + d2 < 1

b2 + e2 < 1

a2 + b2 + d2 + e2 < 1 + (ae - db)2

For any particular image there are 4 different sets of values for (a,b,c,d,e,f) all on the interval [-1,1]. At each iteration step one of the sets is chosen at random to form the next term in the sequence (series).

The results fall into the following broad classes of images

Infnite or constant, these can't be drawn and are specifically tested for and ignored by the software. (These are not affine mappings)
Single blobs
Often with outgoing rays.
Interesting, attractive, and often organic forms.

The third "interesting" category can be further classified as follows

Things made up of intersecting spikes
They often look like Kanji text.

Things that look like
blobs of seaweed on the beach.