drawer.c

int shift(int x, int s) {
    if (s > 0) {
        return x<<s;
    } else if (s < 0) {
        return x>>s;
    } else {
        return x;
    }
}
int bitand(int x, int y) {
    return x&y;
}


for (int i = 0; i < WINDOW_WIDTH; i++) {
    for (int j=0; j< WINDOW_HEIGHT; j++) {
        int r=0;
        int g=0;
        int b=0;
        double xc = -4.2 + 0.01 * (WINDOW_HEIGHT-j); // should max out at 4.2
        double yc = -3.0 + 0.01 * i; // should max out at 3.0
        complex double z = scale*xc + scale*yc*I;
        int trapped = 0;
        int v = 553;
        int iter = 1;

        while (!trapped) {
            v = 36969*bitand(v, 65535)+shift(v, -16);
            double rr = (double)(shift(v, 16)+1)/(pow(2.0,32)+2);
            v = 36969*bitand(v, 65535)+shift(v, -16);
            double s = (double)(shift(v, 16)+1)/(pow(2.0, 32)+2);
            z = (rr*(z*z*z-1)+1)/(s*(z*z-1)+1);
            if (fabs(cabs(z)-1)<0.1) {
                g = 8*iter + (carg(z)+3.14)*44;
                r = 16*iter + (int)fabs((creal(z)-0.893943)*160);
                b = 16*iter + (int)fabs((cimag(z)-0.000110)*1600);
                trapped = 1;
            }
            if (iter > 16) {
                trapped = 1;
            }
            iter += 1;
        }
    }
}

Scott Allen Burns, if you're reading this, I figured it out. I should be using unsigned int, and it wasn't working because I didn't update the return type of my bitwise helper functions. Now I just need to figure out how to do the faux-3d coloring that you do ;)

Also I found the code for coloring it almost exactly like yours:
r = g = b = 256-1000*(fabs(cabs(z)-1)) + (carg(z) > 0 ? 20 : -20);