Here's what I'm using:
Formula: z
k+1 = (|re(z
k)| + |im(z
k)| * i)
2 - c
Algorithm:
Parameters: cX, cY
Let:
x_ = cX, y_ = cY,
eV = 256,
iter = 0,
rsquared = x_ * x_ + y_ * y_,
dzx = 0, dzy = 0; // For accumulating ∂f(c) / dc
while (iter < MAX_ITER AND rsquared < eV) {
// Take absolute values of re and im
_x = x_ < 0 ? -x_ : x_;
_y = y_ < 0 ? -y_ : y_;
// Calculate dz
tmp = 2 * (dzx * _x - dzy * _y) - 1;
dzy = 2 * (dzx * _y + dzy * _x);
dzx = tmp;
// Real part
x_ = _x * _x - _y * _y - cX;
// Imaginary part
y_ = 2 * _x * _y - cY;
rsquared = x_ * x_ + y_ * y_;
}
if (iter < MAX_ITER) {
Let:
r = sqrt(rsquared),
dz = sqrt(dzx * dzx + dzy * dzy),
distance = log(r * r) * r / dz;
if (distance < PIXEL_WIDTH / 20) {
return BLACK;
}
else {
return COLOUR;
}
}
return WHITE;
Can be adapted for Julia set: initialize (x_, y_) to pixel, dz to 1, don't subtract 1 from dz each iteration.
Looks pretty fierce white on black:
burningship-distance-estimate-white-on-black by
c.c.williams, on Flickr
Distance estimation doesn't outline the keel terribly well but works absolutely fine everywhere else, armada towers in particular, which suggests that it's fundamentally good. Works for Julia sets too.
November 28, 2008, 10:27:01 PM
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