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Even 3 years after ~milleniumsentry submit Linear Coil, i'm still amaze by the beauty and the simplicity of this shape and by the strenght of this fractal. (
Suggested by LaraBLN and Featured by
Thanks Kal. In most cases, my images are made with a program called Ultra Fractal. It can be found at [link] The 3d stuff that I have been playing with recently has been made with a program called Mandelbulb. It can be found here: [link]
It's a great suggestion.. I will see if it will work..
It will take a bit though.. slow fractal is slow.
And to illustrate the difference between self similar and self same would require two examples. Self same would be say, a menger cube, where the space the recursive forms are placed into never deviate off of their center points and each new iteration (or set of cubes) fits precisely in the space they are placed in. A cantor set also fits this description.
Self similar (usually) means that the shape being replicated, or the space the shape is being replicated too are incongruant. If you look at the edge of the mandelbrot set, you will note large black globes that encircle it. The subdivision, like the cantor set, is occuring along this line (or what's called the bounds of the set). At regular zoom levels, the globes, while changing in size, look self-same, but they are not. Closer inspection reveals that each one, though having the topology of the main set, deviates from the original by a small amount. The largest hurdle of fractal math, often, is understanding that the further you iterate the formula, the larger these deviations will be, as you are not working with whole numbers, but ever increasingly small slices of a whole number. Even though they represent smaller portions of a whole, the numbers themselves get larger towards infinity, as we are tracking a larger and larger RESOLUTION of division or detail.
These aren't rules however.. more.. guidelines. There are many opportunities to bend the definitions. Flame fractals for instance, have the opportuntity to be self same or self similar, depending on the settings/formula.
This particular piece, is an example of how sometimes, it really is impossible to tell between one or the another. The formula itself is self simlar, but the deviation from iteration to iteration is visibly so minute, that you are lead to believe it's self same.