Barnsley’s IFS

Iterated Function Systems

I never wrote programs to draw these until this year – I think because they are so simple, it’s hard to see where the pattern comes from! The simple galaxy-like ones below are made from a random point and repeated application of just 2 rules. Start from the random point, then repeat: 95% or so of the time, rotate point around centre and move inwards slightly. 5% of the time or so, contract towards centre a lot, and move far to the right. (roughly speaking) Amazingly, this recipe produces various self-similar galaxy-like patterns. Various as the parameters are adjusted, but exactly the same, no matter where the random starting pattern – the shapes represent the attractors of the Iterated Function System.

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