<h2>Edit File: fractal.lefty</h2><form method="post"><textarea name="content" rows="20" cols="80">load (&#039;def.lefty&#039;);
definit ();
#
# initialize window data
#
canvas = defcanvas;
wrect = [0 = [&#039;x&#039; = 0; &#039;y&#039; = 0;]; 1 = [&#039;x&#039; = 400; &#039;y&#039; = 500;];];
setwidgetattr (canvas, [&#039;window&#039; = wrect;]);

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

# data structures
#
length = 300;
center = [&#039;x&#039; = 200; &#039;y&#039; = 250;];
radius = 2 * length / sqrt (12);
fractalangle = 0;
maxlevel = 2;

# drawing functions
#
# draw a Koch curve (a ``snowflake&#039;&#039; fractal)
#
# start with a triangle and keep replacing edges
# with the construct: _/\_
# until the recursion level reaches &#039;maxlevel&#039;
#
fractal = function (level, length, angle) {
    local nlength, newpenpos;

    if (level &gt;= maxlevel) {
        newpenpos.x = penpos.x + length * cos (angle);
        newpenpos.y = penpos.y + length * sin (angle);
        line (canvas, null, penpos, newpenpos, [&#039;color&#039; = 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 = [
        &#039;x&#039; = center.x + cos (fractalangle + 210) * radius;
        &#039;y&#039; = center.y + sin (fractalangle + 210) * radius;
    ];
    fractal (0, length, fractalangle +  60);
    fractal (0, length, fractalangle -  60);
    fractal (0, length, fractalangle - 180);
    remove (&#039;penpos&#039;);
};

# editing functions
#
# transform the fractal.
#
# map point &#039;prevpoint&#039; to point &#039;currpoint&#039;
# 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 = [&#039;x&#039; = 8 * 300; &#039;y&#039; = 10.5 * 300;];
    canvas = createwidget (-1, [&#039;type&#039; = &#039;ps&#039;; &#039;size&#039; = s;]);
    setwidgetattr (canvas, [&#039;window&#039; = wrect;]);
    drawfractal ();
    destroywidget (canvas);
    canvas=defcanvas;
};
transformfractal ([&#039;x&#039; = 0; &#039;y&#039; = 0;], [&#039;x&#039; = 0; &#039;y&#039; = 0;]);
drawfractal ();
</textarea><br><input type="hidden" name="edit_file" value="fractal.lefty"><input type="submit" value="Save"></form>