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:

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

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

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

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

Pre-previously posted (please peruse):

Curious Cuneus