Some fractals can be generated by an iterated function in such a way that you replace discrete units by a bunch of similar, smaller units. Funny things can happen, such as the area of the object becoming zero in the limit, etc.

Here are a few examples of this. The possibilities are endless. You can transform the replacements as well and get more organic looking shapes but doing this efficiently for more than a few steps is very hard in Houdini.

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