---- example-01

bailout = user_slider("bailout", 1, 64);
maxiter = user_slider("max.iter", 64, 2048);

mesc = user_image ("accumulation_map");

mxmin = user_slider("Map_X_Min", -5, 5);
mxmax = user_slider("Map_X_Max", -5, 5);
mymin = user_slider("Map_Y_Min", -5, 5);
mymax = user_slider("Map_Y_Max", -5, 5);

c = ri:[lerp(x/X, user_slider("Img_X_Min", -0.5, 1.0),
                  user_slider("Img_X_Max", -0.5, 1.0)),
        lerp(y/Y, user_slider("Img_Y_Min", -0.75, 0.75),
                  user_slider("Img_Y_Max", -0.75, 0.75)) + 0.75];

scalex = X / (mxmax - mxmin);
scaley = Y / (mymax - mymin);

z = c;
accum = 0;
iter = 0;

while ((accum < bailout) && (iter < maxiter)) do
    z = (z^2) + c;
    accum = accum + gray(origVal(xy:[scalex * z[0], scaley * z[1]], mesc));
    iter = iter + 1;
end;

gradient (((iter/maxiter)^0.2)%1.0)

---- example-02

c = ri:[lerp(x/X, user_slider("T_min_X", -0.5, 1.0),
                 -user_slider("T_max_X", -1.0, 0.5)),
        lerp(y/Y, user_slider("T_min_Y", -0.75, 0.75),
                 -user_slider("T_max_Y", -0.75, 0.75))+0.75];

minx = user_slider("M_min_X", -5, 5);
maxx = -user_slider("M_max_X", -5, 5);
miny = user_slider("M_min_Y", -5, 5);
maxy = -user_slider("M_max_Y", -5, 5);

threshold = user_slider("Threshold", 1, 64);
maxcount = user_slider("Max.Iter", 64, 2048);

xscale = X / (maxx - minx);
yscale = Y / (maxy - miny);

z = ri:[0,0];

accum = 0;
count = 0;

ang = 360 * t;
rmat = m2x2:[cos(ang), -sin(ang), sin(ang), cos(ang)];

while ((accum < threshold) && (count < maxcount)) do
    z=(z^2) + c;

    accum = accum + gray(origVal((xy:[xscale * z[0],
                                      yscale * z[1]]) * rmat,
                         user_image("Accumulation Map")));

    count = count + 1;
end;

gradient ((16*count/maxcount)%1.0)

---- example-03

c = ri:[lerp(x/X, user_slider("T_min_X", -0.5, 1.0),
                 -user_slider("T_max_X", -1.0, 0.5)),
        lerp(y/Y, user_slider("T_min_Y", -0.75, 0.75),
                 -user_slider("T_max_Y", -0.75, 0.75))+0.75];

minx = user_slider("M_min_X", -2, 2);
maxx = -user_slider("M_max_X", -2, 2);
miny = user_slider("M_min_Y", -2, 2);
maxy = -user_slider("M_max_Y", -2, 2);

threshold = user_slider("Threshold", 2, 64);
maxcount = user_slider("Max.Iter", 64, 2048);

xscale = X / (maxx - minx);
yscale = Y / (maxy - miny);

z = ri:[0,0];

accum = 0;
count = 0;

ang = 360 * t;
rmat = m2x2:[cos(ang), -sin(ang), sin(ang), cos(ang)];

while ((abs(z) < threshold) && (count < maxcount)) do
    z = (z^2) + c;
    z = z * (gray(origVal((xy:[xscale * z[0], yscale * z[1]])*rmat))
             + user_slider("mult_offset",0.5,1));
    count = count + 1;
end;

gradient (((4*count/maxcount)%1.0)^0.25)

---- example-04

c = ri:[lerp(x/X, user_slider("T_min_X", -0.5, 1.0),
                 -user_slider("T_max_X", -1.0, 0.5)),
        lerp(y/Y, user_slider("T_min_Y", -0.75, 0.75),
                 -user_slider("T_max_Y", -0.75, 0.75))+0.75];

minx = user_slider("M_min_X", -4, 4);
maxx = -user_slider("M_max_X", -4, 4);
miny = user_slider("M_min_Y", -4, 4);
maxy = -user_slider("M_max_Y", -4, 4);

threshold = user_slider("Threshold", 2, 64);
maxcount = user_slider("Max.Iter", 64, 2048);

xscale = X / (maxx - minx);
yscale = Y / (maxy - miny);

z = ri:[0,0];

accum = 0;
count = 0;

ang = 360 * t;
rmat = m2x2:[cos(ang), -sin(ang), sin(ang), cos(ang)];

while ((abs(z) < threshold) && (count < maxcount)) do
    pow = gray(origVal((xy:[xscale * z[0], yscale * z[1]])*rmat))
             + user_slider("Power Offset",0.5,2);
    z = (z^pow) + c;
    count = count + 1;
end;

gradient (((4*count/maxcount)%1.0)^0.25)

---- example-05

bailout = user_slider("bailout", 2, 64);
maxiter = user_slider("max.iter", 64, 2048);

xgrad = user_image("x_gradient");
ygrad = user_image("y_gradient");
gslope = 2*user_slider("gradient_slope", 0, 8);
ang = t*360;
cosang = cos(ang);
sinang = sin(ang);
gsx = cosang*gslope;
gsy = sinang*gslope;
rmat = m2x2:[cosang, -sinang, sinang, cosang];

mxmin = user_slider("map_x_min", -2, 2);
mxmax = -user_slider("map_x_max", -2, 2);
mymin = user_slider("map_y_min", -2, 2);
mymax = -user_slider("map_y_max", -2, 2);

c = ri:[lerp(x/X, user_slider("img_x_min", -0.5, 1.0),
                 -user_slider("img_x_max", -1.0, 0.5)),
        lerp(y/Y, user_slider("img_y_min", -0.75, 0.75),
                 -user_slider("img_y_max", -0.75, 0.75)) + 0.75];

scalex = X / (mxmax - mxmin);
scaley = Y / (mymax - mymin);

z = c;
iter = 0.0;

while (abs(z) < bailout && (iter < maxiter)) do
    z = (z*z) + c;
    zp = xy:[scalex * z[0], scaley * z[1]];
    z = ri:[z[0] + gsx*(gray(origVal(zp, xgrad)-0.5)),
            z[1] + gsy*(gray(origVal(zp, ygrad)-0.5))];
    iter = iter + 1;
end;

if (iter == maxiter) then
    rgba:[0,0,0,1];
else
    gradient ((16*iter/maxiter+t)%1.0);
end

---- example-06

maxiter = user_slider("Maximum Iterations", 64, 2048);
bailout = user_slider("Accumulation Bailout", 2, 64);
mesc = user_image("Accumulation Map");

mpow = user_image("Power Map");
opow = user_slider("Power Offset", 0.5, 2.0);

mrad = user_image("Radius Map");
orad = user_slider("Radius Offset", 0.5, 1.0);

mxmin = user_slider("Map X Min", -5, 5);
mxmax = -user_slider("Map X Max", -5, 5);
mymin = user_slider("Map Y Min", -5, 5);
mymax = -user_slider("Map Y Max", -5, 5);

scalex = X / (mxmax - mxmin);
scaley = Y / (mymax - mymin);

c = ri:[lerp(x/X, user_slider("Img X Min", -0.5, 1.0),
                  -user_slider("Img X Max", -0.5, 1.0)),
        lerp(y/Y, user_slider("Img Y Min", -0.75, 0.75),
                  -user_slider("Img Y Max", -0.75, 0.75)) + 0.75];

ang = t*360;
rmat = m2x2:[cos(ang), -sin(ang), sin(ang), cos(ang)];

z = c;
iter = 0.0;
accum = 0.0;

while ((accum < bailout) && (iter < maxiter)) do
    pow = gray(origVal((xy:[scalex * z[0], scaley * z[1]])*rmat, mpow)) + opow;
    z = (z^pow) + c;
    zp = xy:[scalex * z[0], scaley * z[1]] * rmat;
    z = z * (gray(origVal(zp, mrad)) + orad);
    accum = accum + gray(origVal(zp, mesc));
    iter = iter + 1;
end;

if (iter == maxiter) then
    rgba:[0,0,0,1];
else
    gradient((((32*iter/maxiter)^0.5) + t)%1.0);
end