Curiouser and Cuneuser

This fractal is created by taking an equilateral triangle, then finding the three points halfway, i.e. d = 0.5, between the centre of the triangle and the midpoint of each side. Using all these points, plus the three vertices, seven new triangles can be created from the original. The process is then repeated with each new triangle:

7triangle

When sub-triangles are discarded, more obvious fractals appear, including this tristar, again using d = 0.5:

tristar

However, a simpler fractal is actually more fertile. This cat’s-cradle is created when d = 0.5:

catscradle

But as d takes values from 0.5 to 0, a very familiar fractal begins to appear: the Sierpiński triangle:

catscradle_expanding

When the values of d become negative, from -0.1 to -1, this is what happens:

catscradle_expanding_to_cuneus

Pre-previously posted (please peruse):

Curious Cuneus

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