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Edit File: fractal.lefty

load ('def.lefty');
definit ();
#
# initialize window data
#
canvas = defcanvas;
wrect = [0 = ['x' = 0; 'y' = 0;]; 1 = ['x' = 400; 'y' = 500;];];
setwidgetattr (canvas, ['window' = wrect;]);

sq = function (x) {
    return x * x;
};

# data structures
#
length = 300;
center = ['x' = 200; 'y' = 250;];
radius = 2 * length / sqrt (12);
fractalangle = 0;
maxlevel = 2;

# drawing functions
#
# draw a Koch curve (a ``snowflake'' fractal)
#
# start with a triangle and keep replacing edges
# with the construct: _/\_
# until the recursion level reaches 'maxlevel'
#
fractal = function (level, length, angle) {
    local nlength, newpenpos;

if (level >= maxlevel) {
        newpenpos.x = penpos.x + length * cos (angle);
        newpenpos.y = penpos.y + length * sin (angle);
        line (canvas, null, penpos, newpenpos, ['color' = 1;]);
        penpos = newpenpos;
        return;
    }
    nlength = length / 3;
    fractal (level + 1, nlength, angle);
    fractal (level + 1, nlength, angle + 60);
    fractal (level + 1, nlength, angle - 60);
    fractal (level + 1, nlength, angle);
};
drawfractal = function () {
    clear (canvas);
    setpick (canvas, center, wrect);
    penpos = [
        'x' = center.x + cos (fractalangle + 210) * radius;
        'y' = center.y + sin (fractalangle + 210) * radius;
    ];
    fractal (0, length, fractalangle +  60);
    fractal (0, length, fractalangle -  60);
    fractal (0, length, fractalangle - 180);
    remove ('penpos');
};

# editing functions
#
# transform the fractal.
#
# map point 'prevpoint' to point 'currpoint'
# with respect to the center of the fractal.
#
transformfractal = function (prevpoint, currpoint) {
    local prevtan, currtan, prevradius, currradius;

prevtan = atan (prevpoint.y - center.y, prevpoint.x - center.x);
    currtan = atan (currpoint.y - center.y, currpoint.x - center.x);
    fractalangle = fractalangle + (currtan - prevtan);
    prevradius = sqrt (
        sq (prevpoint.y - center.y) + sq (prevpoint.x - center.x)
    );
    currradius = sqrt (
        sq (currpoint.y - center.y) + sq (currpoint.x - center.x)
    );
    radius = radius / prevradius * currradius;
    length = radius / 2 * sqrt (12);
};

# user interface functions
#
# bind changes to the fractal to user actions
#
leftup = function (data) {
    transformfractal (data.ppos, data.pos);
    drawfractal ();
};
dops = function () {
    local s;

s = ['x' = 8 * 300; 'y' = 10.5 * 300;];
    canvas = createwidget (-1, ['type' = 'ps'; 'size' = s;]);
    setwidgetattr (canvas, ['window' = wrect;]);
    drawfractal ();
    destroywidget (canvas);
    canvas=defcanvas;
};
transformfractal (['x' = 0; 'y' = 0;], ['x' = 0; 'y' = 0;]);
drawfractal ();