It's a very basic fractal. (Also known as a Sierpinski gasket.) Take an equilateral triangle. Divide into 4 smaller equilateral triangles. Remove the center one. Recursively apply to the remaining 3. It quickly approaches something with an infinite border but zero surface area. A Menger sponge (http://mathworld.wolfram.com/mimg1726.gif) is a related, three-dimensional concept.
The same shape is created if you take Pascal's triangle (http://www.alunw.freeuk.com/pascal.html) and separate it into even and odd components.
They can also be generated through cellular automata, which is what I was thinking of here. Like Conway's Life, but one-dimensional. If a cell has one or two neighbors, turn it on, else turn it off. If you start with a single cell and plot the result into the second dimension, you get a Sierpinski triangle. If you start with random cells turned on, you end up with something like the seashell I linked to above.
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It's a very basic fractal. (Also known as a Sierpinski gasket.) Take an equilateral triangle. Divide into 4 smaller equilateral triangles. Remove the center one. Recursively apply to the remaining 3. It quickly approaches something with an infinite border but zero surface area. A Menger sponge (http://mathworld.wolfram.com/mimg1726.gif) is a related, three-dimensional concept.
The same shape is created if you take Pascal's triangle (http://www.alunw.freeuk.com/pascal.html) and separate it into even and odd components.
They can also be generated through cellular automata, which is what I was thinking of here. Like Conway's Life, but one-dimensional. If a cell has one or two neighbors, turn it on, else turn it off. If you start with a single cell and plot the result into the second dimension, you get a Sierpinski triangle. If you start with random cells turned on, you end up with something like the seashell I linked to above.