Rat's Nest 1/ratsnest1.iso/prgmming/c/jhill_pa.cpp

C/C++ Source or Header | 1996-02-19 | 5.7 KB | 124 lines

Newsgroups: sci.fractals,bit.listserv.frac-l

Path: unixg.ubc.ca!nntp.cs.ubc.ca!cyber2.cyberstore.ca!vanbc.wimsey.com!deep.rsoft.bc.ca!sol.ctr.columbia.edu!usc!elroy.jpl.nasa.gov!newncar!noao!CS.Arizona.EDU!zippy.Telcom.Arizona.EDU!mvb.saic.com!ast.saic.com!jupiter!hilljr

From: [e-mail] (Jay R. Hill)

Subject: Re: A warning to DEEPZOOMers

Message-ID: <[e-mail]>

Followup-To: sci.fractals

Keywords: Mandelbrot Set color

Lines: 109

Sender: [e-mail]

Organization: SAIC

References:  <[e-mail]>

Date: Tue, 11 Jan 1994 21:23:07 GMT

Xref: unixg.ubc.ca sci.fractals:2734 bit.listserv.frac-l:2479



In article <[e-mail]>, [e-mail] (Jay R. Hill) writes:

|> Version 0.13 is now ready ...



There are now 133 potential Mandelmaniacs who have gotten their

lastest fix (at my ftp site or by email).



|> Several folk have expressed interest in this project.  If the

|> interest is still there, I may post the source to DEEPZOOM in

|> segments (with discussion of technique).



                       DEEPZOOM - I



              Mandelbrot Set Coloring Method.



One of the most enjoyable things about displaying the Mandelbrot

Set is actually being able to see all the intricate detail after a

lengthy calculation.  This depends on a good choice of palette and

color algorithm.  A good palette is one which has no adjacent colors

differing by such a small amount that we can't tell them apart.



My favorite palettes have no sudden jumps, but instead return

smoothly to the original color.  These provide a continuous sequence

of colors in the display even if the range of banding is great

enough to require more than one pass through the pelette.



Pelettes are defined in the RGB coordinate frame, where intensity

of Red, Green and Blue are specified by values between 0 and 63.

This is an unnatural system for us, so more useful coordinate

systems were invented such as HSV (Hue, Saturation, Value).  Hue

is expressed as an angle in the color wheel.  Saturation specifies

the amount of white or gray in the color.  In DEEPZOOM, I use full

saturation since I want as much color separation as I can get.

Value is a scaling of the intensity ranging from black to full

intensity.



In my early experiments, I used maximum Saturation and let the Hue

range in equal angles around the color wheel.  This resulted in

many adjacent colors being indistinguishable near Blue, Green and

Red.  This color wheel had too few spokes near Cyan, Yellow, and

Magenta.



Consider the sequence of colors from Green to Yellow.  Colors

formed by ramping Red linearly from 0 to 63 have too little Red

in the steps near Green to be noticable.  Larger steps near Green

are needed with smaller steps near Yellow.  So I tried using a

square root (of component/63) scale.  This made larger steps when

the contribution was small.  This scheme is the one I presently

use in DEEPZOOM.



Here is my C++ code for the palette specification.  The global

variable 'scales' is the intensity scale factor equivalent to

Saturation. The special_scale function is simply a square root

which can be changed easily.  I use 108 color values to go around

the color wheel, starting with number 20.  I use XOR to paint the

cursor.  The colors XOR with 255 are chosen from the opposite side

of the color wheel so the cursor is clearly visible.



#define COLORSIZE 18

#define BRIGHTEST 63.9



float scale,scales;

float special_scale(float c){ return(sqrt(c)); }

void SetMyColor(int C, int R, int G, int B){

  float  red, green, blue, biggest, x;

  red=special_scale(R/(float)COLORSIZE);

  biggest=red;

  green=special_scale(G/(float)COLORSIZE);

  if(green>biggest)biggest=green;

  blue=special_scale(B/(float)COLORSIZE);

  if(blue>biggest)biggest=blue;

  // I like my colors bright

  x = scale*BRIGHTEST/biggest;

  red *= x;

  green *= x;

  blue *= x;

  setrgbpalette(C, (int)red, (int)green, (int)blue);

}

void MyPalette(void){

  int C=20,R,G,B;

  scale=scales;

  //  Colors for escapers

  for(R=G=0,B=COLORSIZE; G<COLORSIZE; ++G,++C) SetMyColor(C,R,G,B);//B-C

  for(R=0,B=G=COLORSIZE; B>0; --B,++C)         SetMyColor(C,R,G,B);//C-G

  for(R=B=0,G=COLORSIZE; R<COLORSIZE; ++R,++C) SetMyColor(C,R,G,B);//G-Y

  for(B=0,R=G=COLORSIZE; G>0; --G,++C)         SetMyColor(C,R,G,B);//Y-R

  for(G=B=0,R=COLORSIZE; B<COLORSIZE; ++B,++C) SetMyColor(C,R,G,B);//R-M

  for(G=0,R=B=COLORSIZE; R>0; --R,++C)         SetMyColor(C,R,G,B);//M-B

  // and now for the XOR colors (for the cursor and interior)

  C=255^20;   scale=1.0;

  for(B=0,R=G=COLORSIZE; G>0; --G,--C)         SetMyColor(C,R,G,B);//Y-R

  for(G=B=0,R=COLORSIZE; B<COLORSIZE; ++B,--C) SetMyColor(C,R,G,B);//R-M

  for(G=0,R=B=COLORSIZE; R>0; --R,--C)         SetMyColor(C,R,G,B);//M-B

  for(R=G=0,B=COLORSIZE; G<COLORSIZE; ++G,--C) SetMyColor(C,R,G,B);//B-C

  for(R=0,B=G=COLORSIZE; B>0; --B,--C)         SetMyColor(C,R,G,B);//C-G

  for(R=B=0,G=COLORSIZE; R<COLORSIZE; ++R,--C) SetMyColor(C,R,G,B);//G-Y

  // and make the cursor WHITE over the filements

  setrgbpalette(255 ^ LIGHTGRAY, 63, 63, 63);

  setrgbpalette(255 ^ DARKGRAY, 63, 63, 63);

  setrgbpalette(255 ^ BLACK, 63, 63, 63);

  setrgbpalette(255 ^ WHITE, 0, 0, 0);

}



Warmly,

Jay "It's tonight honey, let's paint the town" Hill

--

{ [e-mail] } begin writeln(3*ln(640320)/sqrt(163):17:15) end.

void main(){double sqrt(), y=1/sqrt(2.), a=.5, m=1,z; int n=0;

for(;m*=2,z=sqrt(1-y*y),y=(1-z)/(1+z),a=a*(1+y)*(1+y)-m*y,n<4;n++);

printf("%17.15lf\n",1/a);}