
It snowed here today! Wheee!
In honor of the White Hexagonal Fluffy Stuff, here's a nice fractal carpet made of hexagons that illustrates how an infinite number of copies of a shape can converge on a larger fixed-area version of the same shape.
This one's generated from about five and a half thousand hexagons, but obviously, you can keep going infinitely far.
The construction rule's simple. You start with one hexagon (with sides of length "one"), and then add half-size hexagons to any free corners. Then repeat, infinitely (with sides of length "one half", "one quarter", and so on).
What the process converges on is a larger completely-filled hexagon with sides of length "three", so the final area is exactly nine times the original.

Hello. This is a fascinating fractal, and the first I have seen quite like it. Is the iterative formula for this one of your own or drawn from elsewhere?
ReplyDeleteI ask also because I am putting together a symposium session, and would very much like to use an image of this; I'm wondering if it is yours, how I should credit it, and if I could get a larger iteration / rendering with the credit not overlapping the shape.
I've looked around a bit for a better way to contact you here and failed, so please feel free to get in touch if you think something could be arranged. My thanks,
- Heath
Hello. This is a fascinating fractal, and the first I have seen quite like it. Is the iterative formula for this one of your own or drawn from elsewhere?
ReplyDeleteI ask also because I am putting together a symposium session, and would very much like to use an image of this; I'm wondering if it is yours, how I should credit it, and if I could get a larger iteration / rendering with the credit not overlapping the shape.
I've looked around a bit for a better way to contact you here and failed, so please feel free to get in touch if you think something could be arranged. My thanks,
- Heath