Mandelbrot set: Difference between revisions

Line 2,637:

/**

ascii Mandelbrot using fixed point integer maths with an ~~"8.8"~~ ~~encoding~~.

ascii Mandelbrot using 16 bits of fixed point integer maths with a selectable fractional precision in bits.

See also line by line equivalent floating point impl to understand the changes needed ...https://github.com/Johnlon/mandelbrot

This is still only 16 bits mathc and allocating more than 6 bits of fractional precision leads to an overflow that adds noise to the plot..

This code frequently casts to short to ensure we're not accidentally benefitting from GCC promotion from short 16 bits to int.

gcc fixedPoint.c -lm

*/

16 bit shorts chosen for preparation for reimplementation as two bytes per number in assembler.

*/

#include <stdio.h>

#include <stdlib.h>

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#include <stdint.h>

#include <string.h>

short s(short i);

short toPrec(double f, int bitsPrecision);

int main(int argc, char* argv[])

{

// chosen to match https://www.youtube.com/watch?v=DC5wi6iv9io

~~short~~ width = 32; // ~~text~~ width of a zx81

int width = 32; // basic width of a zx81

~~short~~ height = 22; // ~~text~~ ~~height~~ of a zx81

int height = 22; // basic width of a zx81

~~short~~ zoom=1; // bigger = finer detail - leave at 1 for 32x22

int zoom=3; // bigger with finer detail ie a smaller step size - leave at 1 for 32x22

// params

short bitsPrecision = 6;

printf("PRECISION=%d\n", bitsPrecision);

short X1 = toPrec(3.5,bitsPrecision) / zoom;

short X2 = toPrec(2.25,bitsPrecision) ;

short Y1 = toPrec(3,bitsPrecision)/zoom ; // horiz pos

short Y2 = toPrec(1.5,bitsPrecision) ; // vert pos

short LIMIT = toPrec(4,bitsPrecision);

// fractal

char * chr = ".~~,'~=+~~:~~;[/<&?oxOX~~# ";

//char * chr = ".:-=X$#@.";

char * chr = "abcdefghijklmnopqr ";

short iters = strlen(chr);

//char * chr = ".,'~=+:;[/<&?oxOX#.";

short maxIters = strlen(chr);

short py=0;

while (py < height*zoom) {

short px=0;

while (px < width*zoom) {

// $380 = 3.5 $240=2.25 $180=1.5 $300=3

short x0 = ((px*~~0x380/zoom~~) / width) - ~~0x240~~;

short x0 = s(s(px*X1) / width) - X2;

short y0 = ((py*~~0x300/zoom~~) / height) - ~~0x180~~;

short y0 = s(s(py*Y1) / height) - Y2;

short x=0;

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short i=0;

~~while~~ ~~(i < iters) {~~

short xSqr;

short ~~xSqr = (x * x) >> 8~~;

short ySqr;

~~short ySqr =~~ (y * y) ~~>> 8;~~

while (i < maxIters) {

xSqr = s(x * x) >> bitsPrecision;

ySqr = s(y * y) >> bitsPrecision;

// Breakout if sum is > the limit OR breakout also if sum is negative which indicates overflow of the addition has occurred

if ((xSqr + ySqr) > 0x400) {

// The overflow check is only needed for precisions of over 6 bits because for 7 and above the sums come out overflowed and negative therefore we always run to maxIters and we see nothing.

// By including the overflow break out we can see the fractal again though with noise.

if ((xSqr + ySqr) >= LIMIT || (xSqr+ySqr) < 0) {

break;

}

short xt = xSqr - ySqr + x0;

y = (((x * y)>>8) * 2 ) + y0;

y = s(s(s(x * y) >> bitsPrecision) * 2) + y0;

x=xt;

i = i + 1;

}

i = i - 1;

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px = px + 1;

}

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}

// convert decimal value to a fixed point value in the given precision

short toPrec(double f, int bitsPrecision) {

short whole = ((short)floor(f) << (bitsPrecision));

short part = (f-floor(f))*(pow(2,bitsPrecision));

short ret = whole + part;

return ret;

}

// convenient casting

short s(short i) {

return i;

}

</lang>

<pre>

$ gcc fixedPoint.c -lm && ./a.out

Output ...

.........,,,,,,,,,,,,,,,,,,,,,,,

PRECISION=6

........,,,,,,,,,,,,,,,,,,,,,,,,

aaaaaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcdcccbbbbbb

.......,,,,''''''''''',,,,,,,,,,

aaaaaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccddcbbbbb

......,,,'''''''~~=<=~'',,,,,,,,

aaaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbegfcdbbb

.....,,'''''''~~~=+[<+~~'',,,,,,

aaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbdccedbb

....,,'''''''~~~=+/ ;==~'',,,,,

aaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbdcccb

....,''''''~~~=x/o& /;:/~'',,,,

aaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbcfdddcccccccccccccccbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbdded

...,''''''~===+[ /=''',,,

aaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbcccccddfcccccccccccccccccccccccbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccc

...''''~= ++::/ /+~''',,

aaaaaaaaaaaaaaaaaabbbbbbbbbbbbbcccccdeccccccccccccccccccccccccccccccbbbbbbbbbbbbbbbbbbbbbbbbbbcc

...'~~~=+[ X / +~''',,

aaaaaaaaaaaaaaaaabbbbbbbbbbfcccccddeccccccccccccccccdddddeeeddddccccccbbbbbbbbbbbbbbbbbbbbbbbbbe

...~~~+:/o =~''',,

aaaaaaaaaaaaaaaabbbbbbbbbbcccccdddccccccccccccccdeddddeefigeeeddddecccccbbbbbbbbbbbbbbbbbbbbbbbb

... :=~''',,

aaaaaaaaaaaaaaaabbbbbbbecccccdddcccccccccccccdddddddddeefhmgfffddddedcccccbbbbbbbbbbbbbbbbbbbbbb

...~~~++/? =~''',,

aaaaaaaaaaaaaaabbbbbbbcccccccdcccccccccccccccdgddddddfeefgjpijjfdddddedccccccbbbbbbbbbbbbbbbbbbb

...'~~~=+; < +~''',,

aaaaaaaaaaaaaaabbbbbccccccdedccccccccccccccdddddddddeeefgkj ojgfedddddeccccccbbbbbbbbbbbbbbbbbbb

...''''~=&::::/ <+~''',,

aaaaaaaaaaaaaabbbbbcccccegeccccccccccccccdeedddddddeeeeghhkp hgheefddddecccccccbbbbbbbbbbbbbbbbb

...,''''''~===+/ /=''',,,

aaaaaaaaaaaaabbbbccccceddcccccccccccccccfddddddddeeeeefmlkr ihheeeedddddgccccccbbbbbbbbbbbbbbbb

....,''''''~~~= / & ?[:&~'',,,,

aaaaaaaaaaaaabbbccccddfcccccccccccccccedddddddddeeegffhnp rpjffeeeiddddcccccccbbbbbbbbbbbbbbb

....,,'''''''~~~=+/ [==~'',,,,,

aaaaaaaaaaaabbbcccddecccccccccccccccddddddddddeeffffgghm jgffeeeegdddccccccccbbbbbbbbbbbbb

.....,,'''''''~~~=+[<+~~'',,,,,,

aaaaaaaaaaabbbccdedccccccccccccccccdddddddddeefffffgghil khggffffeeeddccccccccbbbbbbbbbbbb

......,,,'''''''~~=&=~~',,,,,,,,

aaaaaaaaaaabbccdeccccccccccccccccddddddddeeef ijjhhhkijlo qkihjhgffgngeddcccccccbbbbbbbbbbbb

.......,,,,''''''''''',,,,,,,,,,

aaaaaaaaaabbcddccccccccccccccccdddddddfeeeefgjq lkk p n khhhiqifedcccccccdbbbbbbbbbbb

........,,,,,,,,,,,,,,,,,,,,,,,,

aaaaaaaaaabbccccccccccccccccccddddddefeeeeffgilq plk rrqgeddcccccccdbbbbbbbbbb

aaaaaaaaaabdccccccccccccccccdddhegeeeeeefffghiq mfeeddcccccccdbbbbbbbbb

aaaaaaaaaaccccccccccccccccdddeeeeeeeeeeffffhjklp phfeeddcccccccdcbbbbbbbb

aaaaaaaaabcccccccccccccddddegeeeeeeeeeffffhppp jgggedddccccccccbbbbbbbb

aaaaaaaaabccccccccccddddeefpifffffffffggggik hgfedddcccccccdcbbbbbbb

aaaaaaaaaccccccceddddddeeifl hgggjrhggggghj p qjnfdddcccccccdcbbbbbbb

aaaaaaaabccccddedddddefeefghqnokkloqiqhhhik ifdddcccccccdcbbbbbbb

aaaaaaaaccceddddddddgfeeffghir o n qmjiijo igfedddcccccccccbbbbbb

aaaaaaaaccddedddddeeeeeefgghkq lll lgfddddcccccccdcbbbbbb

aaaaaaaacddddddddeeeeeefhgjol rn geddddcccccccdcbbbbbb

aaaaaaaaedddddddeeeffggojjll hfeddddeccccccdcbbbbbb

aaaaaaaaddddddefffffggmkopmop ngfefdddfccccccdcbbbbbb

aaaaaaaaeeffgihggiihikk hfeefdddeccccccddbbbbbb

aaaaaaaa kigfgefdddecccccceebbbbbb

aaaaaaaaeeffhgjggghhhklqm ligfhefdddeccccccddbbbbbb

aaaaaaaaddddddefffffgggirq hffefdddeccccccdebbbbbb

aaaaaaaahdddddddeefgfggilkjk hfeedddeccccccddbbbbbb

aaaaaaaacddddddddeeeeeefhhhkl lfefdddeccccccdcbbbbbb

aaaaaaaaccddedddddefeeeeffgijo on qfedddcccccccdcbbbbbb

aaaaaaaabcceddddddddegeeefggik r kko jhfedddcccccccdcbbbbbb

aaaaaaaabccccddddddddefeeefijmk jkp kmiijlq qhfedddcccccccccbbbbbb

aaaaaaaaacccccccdddddddeeefh hhghi kjggghil r geddcccccccdcbbbbbbb

aaaaaaaaabccccccccccdddddefgnfgffghggggggghjm lj feddcccccccdcbbbbbbb

aaaaaaaaabccccccccccccccdddeffggeeeefffffggm igfefddcccccccdbbbbbbbb

aaaaaaaaaaccccccccccccccccdddeeeeeeeeeeffffhjm kgfeddcccccccdcbbbbbbbb

aaaaaaaaaabdccccccccccccccccdddfeeeeeeeegffgiikq feeddcccccccebbbbbbbbb

aaaaaaaaaabbccccccccccccccccccdddddegeeeegffgho p nheeddcccccchfbbbbbbbbb

aaaaaaaaaabbbddcccccccccccccccccdddddeeeeeefhm l ki jlnjeddcccccccdbbbbbbbbbb

aaaaaaaaaaabbccecccccccccccccccccdddddddfeeefir jii npm k ohgggineedcccccccdbbbbbbbbbbb

aaaaaaaaaaabbbccdddccccccccccccccccddddddddeeefggggggiik mjhhgfffffedddcccccccbbbbbbbbbbbb

aaaaaaaaaaaabbbcccedfcccccccccccccccdddddddddeegffffgghp hgffgeeeedddccccccccbbbbbbbbbbbb

aaaaaaaaaaaabbbbccccdddcccccccccccccccgdddddddddeegffgil ggfeeeeddddcccccccbbbbbbbbbbbbbb

aaaaaaaaaaaaabbbbbccccdddccccccccccccccfeddddddddeeeefgi l nkqgeeegeddddcccccccbbbbbbbbbbbbbbb

aaaaaaaaaaaaabbbbbbcccccdedccccccccccccccdedddddddeeeeeghik khhfeefdddddeccccccbbbbbbbbbbbbbbbb

aaaaaaaaaaaaaabbbbbbccccccdddcccccccccccccddedddddddeeefigil jggfedddddddcccccbbbbbbbbbbbbbbbbbb

aaaaaaaaaaaaaaabbbbbbbcccccccdccccccccccccccdefdddddeeeffhlliimfdddddedccccccbbbbbbbbbbbbbbbbbbb

aaaaaaaaaaaaaaaabbbbbbbccccccdddccccccccccccccdddddddeeefg jggheddddedccccccbbbbbbbbbbbbbbbbbbbb

aaaaaaaaaaaaaaaabbbbbbbbbccccccdddccccccccccccccdedddddefgiffeeddddeccccccbbbbbbbbbbbbbbbbbbbbbb

aaaaaaaaaaaaaaaaabbbbbbbbbbecccccdeeccccccccccccccceddddeffegddddgcccccbbbbbbbbbbbbbbbbbbbbbbbbb

aaaaaaaaaaaaaaaaaabbbbbbbbbbbbcccccdddcccccccccccccccccddddddddccccccbbbbbbbbbbbbbbbbbbbbbbbbbbc

aaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbccccddeccccccccccccccccccccccccccbbbbbbbbbbbbbbbbbbbbbbbbbbbbed

aaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbccceddcccccccccccccccccccbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccd

aaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbdcccccccccbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbecccc

aaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbccdebb

aaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbdfccbbb

aaaaaaaaaaaaaaaaaaaaaaaaabbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbcgdccbbbb

</pre>