Fractal Home
Fractal Breeder
including Superfractals based on Michael Barnsley’s work. The Fractal Breeder crosses two IFS fractals and shows their offspring generation by generation. Its focus is the V-variable IFS: fractals with partial self-similarity that lie between strictly self-similar IFS fractals and fully random ones. An integer V limits how many different shapes can occur at each scale. The simpler modes of the machine are morphing, random crossover and condensation.
Parents & Breeding
Display
Using the breeder
In the program, A and B are the two IFS of the super-IFS. On every level each of the V “buffers” randomly chooses A or B. The probability of B grows with the generation, from pure A in generation 0 to pure B in the last one. Each map of the chosen IFS receives an independently drawn buffer of the next level as its sub-picture. “New random seed” draws another member of the same superfractal. The small row of V pictures shows the buffers of the current generation, and a click displays one of them in the main window. The image is plotted by a random descent through this buffer hierarchy, a pointwise variant of the set-based algorithm in the papers. Tap the main window left or right to view all members.
The other modes are simpler.
- Morphing blends the maps of A and B.
- Random crossover takes each map from either parent.
- Condensation A→B uses A as the base figure and applies the maps of B to it g times, so that many copies of A appear, arranged like the attractor of B.
- The Mutation slider adds random variation in these three modes. In condensation it shifts the fixed points of B.