Re: Fractals ASM?

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Re: Fractals ASM?

let's see, I made a Sierpinski variant.. It was rather slow in basic
so I redid it in zshell. (ti-85).


You run the program, and it begins building the fractal. you hit exit,
and you drop back to the zshell menu. no zooming, etc. The main
problem is the fact that the fractals that I find interesting (Z^6-1
NR, and stuff like that), all work with loads of colors :-(. You are
kinda limited to Sierpinski type (A load of random dots, and a point
that goes halfway towards a one of those dots (randomly picked), and
repeat that forever.)

I suppose I might write one that draws the famed leaf/fern. It's also
a sierpinski variant.

If you want the one I have now (with source, so you can see what's
happening), e-mail me.

R dot Zwitserloot at BTInternet dot com


Or, alternatively, write yourself one. this should be fairly easy,
keeping in mind that shifting to the right is dividing by 2, and
shifting left is multiplying by 2.

procedure for a sierpinski:

clear the screen.

Draw x number of dots (for the famed sierpinski triangle, 3, the
corners of your triangle).

now take a point anywhere on the screen. color it white.

Repeat until someone presses exit: (select one of your x number of
dots at random. move your point halfway to it, and color this white
again.)

and after a while you can see the sierpinski forming. Most 'colorless'
fractals are of this type.

Other types:

Iteration fractals: (Mandelbrot and Julia sets)
-----------------------------------------------------------------------
 iterate Znew = Z^2 + C. where Z starts out as being 0+0i, and C is
x+yi, where x is the x-coord and y is the y-coord. i, that's right,
make it a complex plane. keep iterating until you either hit your max
iterations, or until x^2+y^2 exceeds 4. make the brightness relative
to how many times you needed to iterate before it flies off to
infinity (vector exceeds 4).

Iterative fractals are fairly quickly calculated.



Newton Fractals:
----------------------------------------
(NOTE: I ran across this one, I haven't seen it anywhere else, so, who
knows, maybe I discovered/invented a fractal (?).)
This is slooowww but is very special. While you can find the actual
set within itself in iteration fractals (ie: keep zooming and you run
into the mandelbrot again), the newton fractal never repeats itself as
you zoom. yet, you can zoom on and keep getting new stuff infinitely.
This is personally my fave fractal.

do newton/raphson method of approximating roots on a complex function
with all distinct roots. ie: Z^6 -1. repeat for every pixel:

keep approximating until:

1. you reached maximum iterations. color it black.
2. your mathematical equations ran into division by 0. color black.
3. you are within 0.1 of a root. color it whatever you assigned to
this root (ie: red for root 1, blue for root 2, green for root 3,
yellow for root 4, purple for root 5, and orange for root 6), and make
the color darker relative to the amount of iterations it took.


There are some other types, aside from the Sier, Iter, and newt types.
I've heard of int fractals.. don't know how they work though.



<---------- big fractal freak :-P.

for more info, mail me, or do some searching on the net.
I also have a program that allows you to zoom up to 15000x times, with
the mouse, requires vga and a coprocessor (ie: 8087,80287,80387, or
486+). (currently only the newton Z^6-1 one, though I have my Julia
one almost ready (The mandelbrot set is a specific example of a julia
set.)
References: