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Although it does not appear to be widely used, I occasionally see the acronym FASS used to describe certain curves that are space-filling, self-avoiding, simple, and self-similar.

What is the difference between a curve that is self-avoiding and simple in this context?

I've seen multiple references that cite a 1990 paper [1] when using this acronym but I can't find it available anywhere. I was assuming that a simple curve is one that does not intersect itself -- but perhaps it means something different in this context?

[1] P. Prusinkiewicz, A. Lindenmayer, and F.D. Pracchia. Synthesis of space-filling curves on the square grid. To appear in Proceedings of FRACTAL '90, the Ist IFIP conference on fractals, Lisbon, Portugal, June 6-8, 1990.

David
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1 Answers1

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I was able to obtain a copy of the paper referenced. This appears to be the original use of the FASS acronym. The authors define the two terms in question as such:

Self-avoidance -- the segments of the curve do not touch nor intersect.

Simplicity -- the curve can be drawn by a single stroke of the pen, without lifting the pen nor drawing any segments more than once.

So, it appears the authors are using two terms to capture (respectively) the injective and continuous properties, while a more standard definition of a "simple curve" already includes both these properties.

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David
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