Color scheme change (Red to Yellow for now by limiting hue space range to 1/6 the original.. for black to red to yellow I think we have to define some other color space other than HSV which I am using now) plus some minor modifications:
1. define r as local in Plot() since I prefer overriding the plot key as was in the original code by danielmewes.
2. Flip Y axis
3. tune rangee to improve contours and logarithmic abs value tracking mask (I think both r and initial rangeee values should be configurable.. later on maybe we will implement setup screen)
4. also fixed RE contour to grey and IM contour to white for this version.
Example plot of (X+2)^2*(X-1-2*i)*(X+i), in the range +/- 4, +/- 3i:
Code below:
Code:
// SetHSV() and GetColor() based on a
// c++ program from :
// http://commons.wikimedia.org/wiki/File:Color_complex_plot.jpg
// by Claudio Rocchini
// http://en.wikipedia.org/wiki/Domain_coloring
SetHSV(h,s,v);
GetColor(v);
EvalF();
EXPORT Plot()
BEGIN
local x1,x2,y1,y2,co;
local dx:=(Xmax-Xmin)/320;
local dy:=(Ymax-Ymin)/240;
local z1;
local a,b,b1,d,k,x,y;
local r:=4; //r is size of initial square which is 2^r by 2^r pixels
d:=2^r;
FOR x FROM 0 TO 320-d STEP d DO
FOR y FROM 0 TO 240-d STEP d DO
z1:=Xmin+x*dx+i*(Ymin+(240-d-y)*dy);
co:=EvalF(z1);
RECT_P(G0,x,y,x+d-1,y+d-1,co);
END;
END;
IF r THEN
FOR k FROM 1 TO r DO
d:=2^(r-k);
FOR x FROM 0 TO 160/d-1 DO
FOR y FROM 0 TO 120/d-1 DO
a:=x*2*d; b:=y*2*d; b1:=(120/d-1-y)*2*d+d;
z1:=Xmin+a*dx+i*(Ymin+b1*dy);
co:=EvalF(z1);
RECT_P(G0,a,b,a+d-1,b+d-1,co);
z1:=z1+d*dx;
co:=EvalF(z1);
RECT_P(G0,a+d,b,a+2*d-1,b+d-1,co);
z1:=z1+i*d*dy;
co:=EvalF(z1);
RECT_P(G0,a+d,b-d,a+2*d-1,b-1,co);
END;
END;
END;
END;
FREEZE;
WAIT(-1);
END;
EvalF(z)
BEGIN
IF RE(z) THEN
RETURN(GetColor(F1(z)));
ELSE
RETURN(GetColor(F1(z+.001)));
END;
END;
SetHSV(h, s, v)
BEGIN
LOCAL r, g, b;
LOCAL z, f, p, q, t, i;
IF(s==0) THEN
r:=v;
g:=v;
b:=v;
ELSE
IF(h==1) THEN h := 0; END;
z := FLOOR(h*6);
i := IP(z);
f := h*6 - z;
p := v*(1-s);
q := v*(1-s*f);
t := v*(1-s*(1-f));
CASE
IF i==0 THEN r:=v; g:=t; b:=p; END;
IF i==1 THEN r:=q; g:=v; b:=p; END;
IF i==2 THEN r:=p; g:=v; b:=t; END;
IF i==3 THEN r:=p; g:=q; b:=v; END;
IF i==4 THEN r:=t; g:=p; b:=v; END;
IF i==5 THEN r:=v; g:=p; b:=q; END;
END;
END;
r :=MIN(255,IP(256*r));
g :=MIN(255,IP(256*g));
b :=MIN(255,IP(256*b));
RETURN RGB(r,g,b);
END;
GetColor(v)
BEGIN
LOCAL a:=0;
LOCAL m,ranges,rangee,k,sat,val;
IF v≠0 THEN a:=ARG(v); END;
WHILE (a<0) DO a := a+ (2*π); END;
a := a/(2*π);
// RE Contour
m := ABS(RE(v));
ranges := 0;
rangee := 0.5;
WHILE(m>rangee) DO
ranges := rangee;
rangee := rangee * e;
END;
k:=(m-ranges)/(rangee-ranges);
IF (k<0.5) THEN
sat:=k*2;
ELSE
sat:=1 -(k -0.5) *2;
END;
val := sat;
sat := 1 - (1-sat)^3; sat := 0.4 + sat*0.6;
val := 1 - val;
val := 1 - (1-val)^3;
val := 0.6 + val*0.4;
IF (val > 0.9999) OR (sat >0.9999) THEN
//return SetHSV(a/6,sat,val);
return RGB(200,200,200);
END;
//IM Contour
m := ABS(IM(v));
ranges := 0;
rangee := 0.5;
WHILE(m>rangee) DO
ranges := rangee;
rangee := rangee * e;
END;
k:=(m-ranges)/(rangee-ranges);
IF (k<0.5) THEN
sat:=k*2;
ELSE
sat:=1 -(k -0.5) *2;
END;
val := sat;
sat := 1 - (1-sat)^3; sat := 0.4 + sat*0.6;
val := 1 - val;
val := 1 - (1-val)^3;
val := 0.6 + val*0.4;
IF (val > 0.9999) OR (sat >0.9999) THEN
//return SetHSV(a/6,sat,val);
return RGB(255,255,255);
END;
//Domain Coloring
m := ABS(v);
ranges := 0;
rangee := 0.01;
WHILE(m>rangee) DO
ranges := rangee;
rangee := rangee * e;
END;
k:=(m-ranges)/(rangee-ranges);
IF (k<0.5) THEN
sat:=k*2;
ELSE
sat:=1 -(k -0.5) *2;
END;
val := sat;
sat := 1 - (1-sat)^3; sat := 0.4 + sat*0.6;
val := 1 - val;
val := 1 - (1-val)^3;
val := 0.6 + val*0.4;
return SetHSV(a/6,sat,val);
END;
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