# Fractals

Is there anybody out there interested in the fractals of nature. About how you could build plants, trees, clouds and more?
I would like to discuss and share code!

Martin

Well, I don’t have any code, but I did see a neat idea recently in a book about fractals (it was called fractals: building blocks of chaos, or something like that):

In order to make a nice looking needle-tree (as opposed to a tree with leaves), you take the basic Pythagorian figure - triangle and 3 squares surrounding it. Now you take the two squares on the cathedes and use as as the hypothenuse square of a new figure. By doing this you can get a pretty nifty pciture; it even looks tree-like with just the outlines drawn. Just imagine it with textures and whatnot.

Hope this is what you were looking for!

I don’t know, and can’t find, the word “cathedes”. Did you mean something else? Can you give a more complete explanation of the method of construction? Thanks,
Barry

He meant “catets”. My english is too poor to describe it w/o drawing.

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This two segments(bottom and left) that are orthogonal are “cathedes”.

The adjecent and oposite sides used in trig then, I see.

One cool fractal thing I have heard of was mathematicly making a human face and later an entire human body with some simple equations. The thing is that most humans are perfectly symmetrical, those that aren’t are supposedly ugly- lopsided face, broken nose, ripped ear etc… The body is built using a constant called phi (not PI). It comes from the fibanachi(sp?) sequence: 1,1,2,3,5,8,13,21,34,55 and so on (the previois 2 numbers added together. If you divide the last number by the second last, 55 /34 = 1.6176. As the sequence continues it gets more acurate. And so the human body is built ti this ratio: your height /height to navel = phi, width of nose/ width of mouth = phi. In this way an entire human body can be made mathematicly and the result should be the most beautifull, perfect human (this should also mean that computer generated porn has a future). Other animal and plants are made with the same constant. The eqyptian pyramids were built with phi as the ratio, base / height = phi. I expect the above mentioned tree would use the ratio.
Interesting but true, now I have got you looking in a mirror with rulers and measuring tape trying to determine if you are ugly or not!

As an old ( literally ) math teacher, let me say that the orthogonal sides are normally called “legs”. What language uses the other word?
Also, Phi is named after the ancient Greek sculptor Phidias who believed ( rightly??? ) that the most perfect body has alot of proportions that match the given number ( Greek statues always seemed rather stocky to my American eye, but it is all a matter of taste ).
The suggested fractal form for creating a tree is interesting and if it can be done faster than other methods it would be really useful.
Barry

If you are really interested in general fractals there is a technique called Perlin Noise that is very good for this sort of thing, check it out here:

Perlin Noise

I got it working today and already I have used it for fractal clouds and general dirt textures.

Fleejay