VEX fx

***************************************************************************************************************************
POWER EIGHT:

//float pi    = $PI;
vector v    = v@P;
vector c    = v@P;
int iterations = chi('iterations');
float n = chf('exponent');
float phase = chf('phase_shift');

for(int i=0; i<iterations; i++){
    float r     = sqrt(pow(v.x, 2) + pow(v.y, 2) + pow(v.z, 2));
    float phi   = n * asin(v.z/ r) + phase;
    float theta = n * atan2(v.y, v.x);

    float newx = pow(r, n) * cos(theta) * cos(phi);
    float newy = pow(r, n) * sin(theta) * cos(phi);
    float newz = pow(r, n) * -sin(phi);

    v = set(newx, newy, newz) * r + c;

    if(length(v) > chf('t')){
        f@density = 0.0;
        f@temperature = 0.0;
    }
}