I made a fractal of my own some tim ago after only a few attempts, but never actually tried to think through the mathematics of how to make the fractal until, well, today. I tried to find a pattern in the lengths of the fractal's structure, but couldn't, so I went back to the original idea of how the fractal is made in the first place. I came up with the following on how to draw it:
Quote:
Create a line that is equal to five times a number (5s). Go to one end of the line and draw two diagonals in such a way that the line bisects a 90 degree angle, of a length equal to that of a hypotenuse of an isosceles right triangle with legs of length s. Then, go down by s from the top and draw two more diagonals similarly, and once again go down by s and draw two more diagonals.

Basically, from there you treat each diagonal as the 5s line again.
I managed to discover a few possible patterns, though I could only get up to about the fourth iteration before I became confused...
I found that if you take sets of length and multiply and divide a certain way you come up with something:
Quote:
Let s1 be the first iteration's large line size, say, 40 with s sections of 8. Then let s2 be the second iteration's line size, and then d1 be the first iteration's '90 degree diagonal' size, and d2 be the second iteration's '90 degree diagonal' size. For that, d1/d2 X s1/s2 = s1^1

Then let d3 be the diagonal of the third iteration, and s3 be the third iterations "straight line," and then d2/d3 X s2/s3 = s2^2

I haven't yet worked out what s4 and d4 would be, following the same pattern, but it is possible that d3/d4 X s3/s4 = s3^3


Anyway, I was wondrering if anyone might be able to help me with this, or even if anyone can understand the verbal terming of the way the fractal has to be drawn in the first place...

One more thing. I called my fractal "the arrow fractal" because that's basically what it looks like.