chaos by blob of gate
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			        docs
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	welcome to the world of chaos. this program calculates
mandelbrot and julia groups, geometrical fractales of the nature.
the mandelbrot and julia groups are chaotical; you newer cannot tell
the exact color of the pixel in the group. when you add the calculating
accuracy and iteration, the color of the pixel will come nearer to the
right color, but the exact color never can be calculated.
when you zoom the fractal, it will reveal more and more new features.
only the accuracy of the program will limit the zooming.
most natural landscapes are also fractals: when you look closer and
closer to the landscape it has also unlimited number of new features.
tree will first reveal brances, then little brances, tree cells,
molecules and even atoms. in the program the black pixels are
the part the group. other pixels are in the borders of the group.

			algorithms

	the coordinates of the mandelbrot (and nearly always also of the
julia) group are x (-2.0 to 0.5) and y (-1.2 to 1.2) the program
supports decimal numbers from -3.99999999 to 3.99999999 which is more
than enough. the center of the mandelbrot group is 0 , 0.
program used 16 bit accuracy if possible (faster) and 32 bit
accuracy (slower) if area is smaller than 0.09 . 32 bit accuracy allows
zooming to 0.0000005 maxium. that is zoom * 1000000 !!! if the width of
the group would be 10 cm * 10 cm the maxium zoom would show the area of
50 nm * 50 nm. and one pixel would show area of 150 pm * 150 pm
( aproximate as wide as the width of an atom!!)

	the complex number c ( (= x+y*i) where x is x-coordinate, y is
y-coordinate and i is squarefoot -1 (confusing??) .)
is a part of the mandelbrot group, if

z = 0
repeat n times (n = iteration)
z = z²+c

doesn't overflow and grow towards infinity. in the program, the limit
is 4. result of 4 overflows.

algorithm of the julia is similar, but c is static and can be given
in the beginning.

z = (x+y*i)
repeat n times (n = iteration)
z = z²+c


			the program

	when you run the program it will first ask some basic values.
return indicates previous value to be used.

error correct - means how exact the color of the pixel is.
		0 means only 1 calculation per pixel
		1 means 2 calculations per pixel
		2 means 3 calculations per pixel. the most accuratic.
		using more accuracy consumes speed !

number of bpls- number of colors in the picture 2,4,8,16 or 32
		bpls up to 4 doesn't consume speed.

cr	      - is the real (x) part of the complex number c
		to use mandelbrot type x here.
		to use julia type any decimal number from -3.999 to 3.999
		for example:	0.3283691, 0.29296875, 0.277099609
				-0.915527343 and 0

ci	      - is the image (y*i) part of the complex number c
		type 0 here for the mandelbrot group.
		examples:	0.01831054, 0.830078125, 0.6420898 and 0

realfrom and  - x coordinates of the left and right edges of the screen.
realto		exaple: (mandelbrot) from 1.2 to 1.29

image to      - y coordinate of the upper edge of the screen.
		exaple: (mandelbrot) from 0.147

iterations    - how many times each pixel is calculated. should be set
		to 32 at least. maxium 1023.
		great iterations consumes much speed.

		controller keys

	for zooming more in the picture use mouse when the picture
is made. box shows the area to be shown.

keys:	esc	- exit picture mode
	f1	- minimum zoom
	f2	- zoom backwards
	f3	- iteration 32
	f4	- iteration 64
	f5	- iteration 128
	f6	- color palette1
	f7	- color palette2
	f8	- color palette3
	f9	- cycle on/off
	f10	- save picture in iff mode (only when calc finished)
	1 to 9	- cyclespeed
	0	- cycledirect

- when the exit is made decimal numbers indicating x-start, x-stop and
y-start of the previous picture will be typed down to the screen.


		contact me

	this program is shareware. it means if you like it and use
it, please send reasonable amount of money to:

(blob of gate)
henri saarikoski
kutunpolku 3
38200 vammala
finland

tel. 358-32-43678 after 5 o'clock eurotime!

	in return you get the documented source of the program
if you like and routines such as keyboard driver, blitter linedraw,
hardware screen make, iff-save routine and of course mandelbrot
and julia calculation routines.
contact me also for suggestions and intstructions and feel free
to put this program to your collections.
and if you are intrested in role-game graphics making contact
me for co-operation?