Disassembly of a Highly Optimised Fractal Generator - A short explaination of fractals, a simple algorithm and Disassembly of this amazing 31 byte fractal generator.

Disassembly of a Highly Optimised Fractal Generator

Written by:	Geek_Freek
Published by:	SAJChurchey
Published on:	2005-11-26 05:33:00
Topic:	Assembly

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A short explaination of fractals, a simple algorithm and Disassembly of this amazing 31 byte fractal generator.

Well i got sier.com file when i was looking for fractal generators.

Let me start of with Fractals

FRACTALS

Wikipedia defines it as :

A fractal is a geometric object which is rough or irregular on all scales of length, and so which appears to be 'broken up' in a radical way.

The Sierpinski Triangle(and how its related to Pascal's Triangle)

Well, if you were to plot the Pascals triangle, substitute every odd number with a black dot and every even number with a white dot... you'll end up with the Sierpinski triangle.

Algorithm to generate Sierpinski's Triangle

1 : Choose any three arbitary points A,B,C
2 : Select any random point D lying in the triangle ABC.
3 : Select any E = random_point(A or B or C).
4 : D = midpoint b/w D and E
5 : Mark D with dark point.
6 : Goto 3

I suggest you see this if you haven't already. Lets get down to disassembling it.

Disassembly of Sier.com

1: ; This file is generated by The Interactive Disassembler (IDA)
2: ; Freeware version
3: ; Copyright (c) 2000 by DataRescue sa/nv, http://www.datarescue.com
4: ; File Name : D:ASMSIER.COM
5: ; Format : MS-DOS COM-file
6: ; Base Address: 1000h Range: 10100h-1011Fh Loaded length: 1Fh
7:
8: ; Segment type: Pure code
9: seg000 segment byte public 'CODE'
10:          assume cs:seg000
11:          org 100h
12:          assume es:nothing, ss:nothing, ds:seg000
13:
14: ;-Subroutine-------------------------
15:
16:          public start
17: start proc near
18:          mov ax, 13h
19:          int 10h ; - VIDEO - SET VIDEO MODE
20:                      ; AL = mode
21:          mov bx, 3
22:          mov si, 0A0A0h
23:          mov ds, si
24:          assume ds:nothing
25:
26: loc_0_10D: ; CODE XREF: start+17j
27:          mov cx, 0C8Bh ; loc_0_10D + 1 = mox cx,[si]
28:          xor ch, [bx+si]
29:          mov [si-13Eh], ch
30:          dec si
31:          jnz near ptr loc_0_10D+1
32:          int 16h ; KEYBOARD - READ CHAR FROM BUFFER, WAIT IF EMPTY
33:                      ; Return: AH = scan code, AL = character
34:          xchg ax, bx
35:          int 10h ; - VIDEO - SET VIDEO MODE
36:                      ; AL = mode
37:          retn
38: start endp
39:
40: seg000 ends
41:
42:
43:          end start
44:

Heres what I figured

We move A0A0 to SI.. which is the video buffer
Only during initialization (line 27) works as mov cx,0C8Bh. Then onwards it is used as mov cx,

The next point to mark is figured out using line 28 and 29. I dont understand how the XORing works. Leave a comment if you do.
Line 29 seems to be marking the point.

Conclusion
I have no idea who the author of the program is. It is nonetheless a work of art. If you find a way to compress it further, you have my respect. Also I have not understood exactly how the point to be marked is found, and it isn't according to the algorithm I listed earlier (or is it?). The XOR seems to be a shortcut to generate this point. BX remains fixed at 3. SI is decremented every loop.

Leave a comment if you figure anything of this mystery.

Geek
(c)Anil Gulecha

Did you like this article? There are hundreds more.

Comments:

telekinetic
2005-11-29 12:08:17

I once wrote a program to draw a Sierpinski's triangle, but it was a recursive implementation. This is pretty impressive though.

Anonymous
2005-11-30 07:30:17

ANYONE figured the lines 28,29??

santa
2005-12-03 12:50:59

hum..... far too geeky for me.

yonatan
2005-12-31 07:03:35

xor stuff works like this I think

putpixel( somex, somey ); // low point in triangle - mov cx, 0C8Bh

for( y = maxy; y; y-- ) {
for( x = maxx; x; x-- ) {
if( getpixel( x+1, y ) XOR getpixel( x-1, y ) ) {
putpixel( x, y-1 );
}
}
}

yonatan
2005-12-31 07:05:04

damn.. I meant like this..

putpixel( somex, somey ); // low point in triangle - mov cx, 0C8Bh

for( y = maxy; y; y-- ) {
   for( x = maxx; x; x-- ) {
      if( getpixel( x+1, y ) XOR getpixel( x-1, y ) ) {
         putpixel( x, y-1 );
      }
   }
}

Anonymous
2006-01-19 00:25:07

The XOR is to generate the triangle line by line (it doesn't use the midway method). On the first line you put a black pixel. The second line is the first line put through an XOR with the 2 neighbouring pixels being the inputs. See cellular automata for more information

anilg
2006-01-19 09:09:42

Hmm.. thanks.. i'll look into it and add to the article accordingly.

Thanks again

anilg
2006-01-19 09:21:37

And while i understand the stuff and integrate it:

http://www.dms.umontreal.ca/~andrew/Binomial/cellautom.html

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