MathMap Examples

You can find lots of examples of MathMap generated images at the very interesting and well-written page about visualizing complex functions by Hans Lundmark.

Alexander Heide has used MathMap to transform x-ray images of crystals.

Tom Rathborne has used MathMap to generate some very unusual Mandelbrot fractal images.

Laurent Despeyroux has a page with GIMP tutorials which make use of MathMap to create interesting effects.

The following are examples of MathMap expressions, together with their effect on two images. The left one is an image of Elisa Bridges (US Playmate of the Month December 1994), the right one is a grid with grid size 16. All these expression are included in the plug-in.

The original images:

origVal(xy+xy:[sin(y/6),sin(x/6)]*3)

origVal(xy+xy:[5*sign(cos(y/6)),5*sign(cos(x/6))])

origVal(xy*xy:[cos(pi/2/Y*y),1])

origVal(ra+ra:[sin(r/3)*3,0])

origVal(ra+ra:[0,-(r/R-1)*pi/5])

origValRA(r,a+a%0.14-0.07)

origValRA(r*r/R,a)

The result of this expression depends on the gradient and on the value of t.

gradient((gray(origVal(xy))+t)%1)

The result of this expression depends on the setting of the curve.

p=origValXY(x,y);
rgbaColor(curve(red(p)),curve(green(p)),curve(blue(p)),alpha(p))

As does this (there are actually two curves here and one slider).

alpha = user_slider("alpha",0,6.28318530);
dir = xy:[cos(alpha),sin(alpha)];
ndir = xy:[-dir[1],dir[0]];
p = xy / m2x2:[dir[0],-ndir[0],
               dir[1],-ndir[1]];
pt = dir * p[0];\nvec = xy - pt;
dist = -p[1] / R;
pos = 0.5 + p[0] / R / 2;
lower = 1 / (user_curve("lower",pos) * 4 - 2);
upper = 1 / (user_curve("upper",pos) * 4 - 2);
f = lower + ((dist + 1) / 2) * (upper - lower);
origVal(pt + ndir * f * R)

origVal(xy+xy:[rand(-3,3),rand(-3,3)])

p=origVal(xy);
p=if inintv((a-(pi/20))%(pi/5),0,(pi/10)) then p else -p+1 end;
if inintv(r%80,68,80) then p else -p+1 end

# Thanks to Herbert Poetzl
rd=0.9*min(X,Y);
if r>rd then
    rgba:[0,0,0,1]
else
    alpha=-(5/3)*pi; beta=(1/3)*pi; gamma=t*pi*2;
    sa=sin(alpha);
    sb=sin(beta);
    ca=cos(alpha);
    cb=cos(beta);
    theta=a;
    phi=acos(r/rd);
    x0=cos(theta)*cos(phi);
    y0=sin(theta)*cos(phi);
    z0=sin(phi);
    x1=ca*x0+sa*y0;
    z1=-sa*-sb*x0+ca*-sb*y0+cb*z0;
    if z1 >= 0 || 1 then
        y1=cb*-sa*x0+cb*ca*y0+sb*z0
    else
        z1=z1-2*cb*z0;
        y1=cb*-sa*x0+cb*ca*y0-sb*z0
    end;
    theta1=atan(-x1/y1)+(if y1>0 then pi/2 else 3*pi/2 end);
    phi1=asin(z1);
    origVal(xy:[((theta1*2+gamma)%(pi*2)-pi)/pi*X,-phi1/(pi/2)*Y])
end

This is an example of combining MathMaps alpha operation with layers. The background is the image of Elisa. The second layer is the grid, which has been MathMapped with the following expression:

origVal(xy)*rgba:[1,1,1,0]+rgba:[0,0,0,sin((r-a*6)/6+t*2*pi)*0.5+0.5]

abs(rgba:[sin(r/4)+sin(15*a),sin(r/3.5)+sin(17*a),sin(r/3)+sin(19*a),2])*0.5

grayColor(sin(x*y/180*pi)*0.5+0.5)

This is a rather sick example of what is possible with MathMap. This image took 7 seconds to render on my Pentium-S 166. The colors do of course depend on the gradient set.

p=ri:(xy/xy:[X,X]*1.5-xy:[0.5,0]);
c=ri:[0,0];
iter=0;
while abs(c)<2 && iter<31
do
    c=c*c+p;
    iter=iter+1
end;
gradient(iter/32)