This fractal, which you can see, as I hope, above, was invented/discovered by W. Gosper. See also Martin Gardner in Scientific American 235 (december), 124-133, "In which < curves force redefenition of the word >curve".

This fractal is obtained by replacing recursivly every sexangle by seven smaller sexangles. In this special case, the sexangles are colored: the sexangle in the middle is colored white, and the rest is colored in blue, green, yellow and so on. In the next step, there is a sexangle colored white-white, white-blue and so on, blue-white, blue-blue and so on, and so on, and so on. As a result, the plane is covered with every possible color, except for the dark ones. In the picture above, we see an iteration broken of at step three.

The pictures which you can see below, are iterations of stage 3, 4, 5 and 6. Iteration step 6 contains details not visible at this resolution, so further iterations would be of no use.

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Jan Thor
www.janthor.com
jan@janthor.de