This approach, applying all the transformations to the entire picture, is called the Deterministic Algorithm for generating fractals. Here is a more mathemaical treatment.
Another approach for generating the same images is the 1.G. Random Algorithm A precursor to the Random Algorithm is the Chaos Game.
Before investigating the Random Algorithm, or its variant 1.H. Driven IFS useful for uncovering patterns in data, we study the 1.F. Inverse Problem: given a fractal, how can we find the transformations to produce that fractal?
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