I made a new fractal

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I made a new fractal

Postby Keiji » Sun May 27, 2007 5:05 pm

http://fusion-global.org/share/spearfractal.png

I haven't seen this mentioned anywhere before.

The above is iteration 5. I've colored them according to each iteration where black is iteration zero. To form it, you start with the three black triangles, and then for each iteration, you put a copy of the previous iteration at each of the three corners, moving it so that it's the furthest distance away from the center but still touches the rest of the shape.

I called it the "Spear fractal" because it looks like some oddly shaped spear :P
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Postby Nick » Sun May 27, 2007 7:16 pm

Very cool! Try making it with more complex shapes, such as a pentagon, or octagon...
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Postby Keiji » Sun May 27, 2007 7:25 pm

I don't think anything other than a triangle would work, because it requires an odd number of sides (so that each side is opposite a corner) and for the shape to tessellate; the triangle is the only 2D shape that meets these conditions.

What would be interesting to find though is the pattern of the distances overlapped on each iteration. The ones for the first 5 iterations are 0, 0, 1, 4 and 7.
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Postby Asymptote » Mon May 28, 2007 1:01 pm

Nice fractal!
0101010101010101...
0011001100110011...
0000111100001111...
0000000011111111...
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Postby papernuke » Sun Jun 10, 2007 2:42 am

What is a fractal? what does it have to do with science?
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Postby Keiji » Sun Jun 10, 2007 3:06 am

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