Did you know that if you turn the word "fractal" into a fractal, it apparently has dimensionality 1.702?
Well, in this particular image I saw. It didn't specify what type of dimension, and it really depends on the IFS you use. xD
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Mary3d
Whats that mean a dimension of 1.702?
TetrisGuy · 26-30, M
It doesn't specify what type of dimension exactly, but I assume it means Hausdorff Dimensionality or self-similar dimensionality. It's a little hard to explain. xD
Mary3d
Lol its ok : P
TetrisGuy · 26-30, M
It kinda means something like... well... I can explain the self-similarity dimension.
Maybe that's what this is. Hang on. *does a calculation*
Maybe that's what this is. Hang on. *does a calculation*
TetrisGuy · 26-30, M
Yeah I think it refers to the self-similarity dimension anyways. Can't calculate exactly due to the IFS this person used.
http://sprott.physics.wisc.edu/fractals/chaos/FRACTAL.GIF
Basically, the self-similarity dimension is equal to the logarithm of the number of copies made of itself divided by the negative logarithm of the scaling factor. So a fractal, say the Sierpinski triangle, that is made up of 3 copies of itself scaled by factor of a half, would have a dimensionality of log 3/-log(1/2) which equals approximately 1.58.
http://sprott.physics.wisc.edu/fractals/chaos/FRACTAL.GIF
Basically, the self-similarity dimension is equal to the logarithm of the number of copies made of itself divided by the negative logarithm of the scaling factor. So a fractal, say the Sierpinski triangle, that is made up of 3 copies of itself scaled by factor of a half, would have a dimensionality of log 3/-log(1/2) which equals approximately 1.58.