How to draw a shape like below using fractals in tikZ?
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I couldn't resist. This Metapost version might give you some ideas of how to do things in TikZ if that's your chosen approach.
prologues := 3; outputtemplate := "%j%c.eps"; vardef decorate(expr line, ttl) = if ttl > 0: save m, p; pair m; m = point 1/6 of line rotatedabout(point 1/2 of line, 90); path p; p = point 0 of line -- m -- point 1 of line; draw p; decorate(subpath(0,1) of p, ttl-1); decorate(subpath(1,2) of p, ttl-1); fi enddef; beginfig(1); n = 3; path base; base = for i=1 upto n: up scaled 4cm rotated (360/n*i) -- endfor cycle; draw base; for i=1 upto length(base): decorate(subpath (i-1,i) of base, 4); endfor endfig; end.
If you crank up the number of iterations a bit you get some simple fractal self-similarities. Here is it with 5 sides in the base shape and using a depth of 12.