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Hi people,
me again, and there is this polish mathematician in the subject line, too.
This time it's 2d, even simpler, and NO theory question.
Sierpinskis triangle is defined by "ifs" :
take three copies, halve the size, and move them towards the corners of a triangle.

For reasons I can't remember any more (and it was only the beginning of april, talk about loss of memory here) I changed that into:
take three copies, halve the size, rotate n degrees, and move them towards the corners of a triangle.

When n is 0, 120, 240 degrees the well known figure appears!
For n = 60, 180, 300 there is some snowflaky thingie looking like the attached picture.
I had found one or two instances of that thing on the net - can't seem to find it again, but it was only shown, not given a name.
Since for any other angles than those mentioned the result seem to be disconnected (see second attachment, tiny animated gif), you got exactly two connected sets in that series: sierpinski triangle and "TheFlake".

Does anybody know if "TheFlake" has been given an official name?

Thank you for your time
Karl

That gif looks a lot like rotating a transform in a Apophysis Sierpinski Gasket

Fascintaing and beautiful! A snowflake!

Very similar to a Sierpinski Pentagon:
  http://ecademy.agnesscott.edu/~lriddle/ifs/pentagon/pentagon.htm (http://ecademy.agnesscott.edu/~lriddle/ifs/pentagon/pentagon.htm)
or a Durer's Pentagon:
  http://ecademy.agnesscott.edu/~lriddle/ifs/pentagon/Durer.htm (http://ecademy.agnesscott.edu/~lriddle/ifs/pentagon/Durer.htm)

And I have seen Koch Snowflakes that are also very similar.

Sierpinski to AntiSierpinski in Fractracer ("Triangle Rotate" sample)