Thanks for the link to your other fractals (which I edited to remove a spurious space). I’m particularly intrigued by numbers 9 to 11. They look like they’re related to the fractals associated with balanced base 2+i, but you seem to have arrived at them by a different, space-filling route. I’d be interested to know more about the constructions of those ones.

]]>On the other hand, if you take this construction to its limit (as the number of dots approaches infinity), I’m pretty sure the result does exhibit self-similarity, which is the key point of some other definitions of *fractal*. In the limit, the top sub-triangle, for example, will be a curve folded up in exactly the same way as the whole triangle is folded up, only smaller.

I concede that the first iteration of the triflake is a pretty poor approximation of the limit, though.

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