Welcome to Fractal Forums

// set global variables
var tfMult = 2.0;
var tfSub = 1.0;
var cutoff = 1024;
var itMin = 5;
var itMax = 21;
var amplitude = 8;
var thetaAdj = 0.000001;
var phiAdj = 0.0000001;
var radiusMin = 0.32 * d;
var radiusMax = 0.56 * d;

// making a mandelbulb
function bulb() {
    var volume = 0;
    for (var x = 0; x < d; x++) {
        var xc = tf(x);
        for (var y = 0; y < d; y++) {
            var yc = tf(y);
            for (var z = 0; z < d; z++) {
                /*
                * Continue if not in range radiusMin -> radiusMax.
                * This saves a lot of time by not performing 21 iterations
                * on locations that clearly won't have blocks. */
                var r = rfc(x,y,z);
                if (r < radiusMin)
                    continue;
                if (r > radiusMax)
                    continue;
                
                var zc = tf(z);
                
                var iterations = -1;
                var C = new Vector(xc, yc, zc);
                var Z = new Vector(0, 0, 0);
                
                // iterate over vectors
                while ((mag(Z) <= cutoff) && (iterations < itMax)) {
                    Z = add(formula(Z, amplitude), C);
                    iterations++;
                }
                
                // place block if cutoff reached in itMin -> itMax range
                if ((iterations >= itMin) && (iterations < itMax)) {
                    if (r < radiusMin)
                        radiusMin = r;
                    if (r > radiusMax)
                        radiusMax = r;
                    volume++;
                    if (volume % 10000 == 0)
                        context.print("    "+volume+" blocks placed... \n");
                    var vec = new Vector(
                        region.getMinimumPoint().getX() + x,
                        region.getMaximumPoint().getY() + y,
                        region.getMinimumPoint().getZ() + z);
                    if (bt.equals("default"))
                        blocktype = context.getBlock(defaultBlockList[iterations - itMin])
                    else if (bt.equals("wool"))
                        blocktype = context.getBlock(woolBlockList[iterations - itMin])
                    else if (bt.equals("plant"))
                        blocktype = context.getBlock(plantBlockList[iterations - itMin])
                    else if (bt.equals("nether"))
                        blocktype = context.getBlock(netherBlockList[iterations - itMin])
                    else if (bt.equals("jungle"))
                        blocktype = context.getBlock(jungleBlockList[iterations - itMin])
                    else if (bt.equals("mine"))
                        blocktype = context.getBlock(mineBlockList[iterations - itMin])
                    else if (bt.equals("desert"))
                        blocktype = context.getBlock(desertBlockList[iterations - itMin])
                    else if (bt.equals("city"))
                        blocktype = context.getBlock(cityBlockList[iterations - itMin])
                    else if (bt.equals("cabin"))
                        blocktype = context.getBlock(cabinBlockList[iterations - itMin])
                    else if (bt.equals("test")) {
                        blocktype = context.getBlock(testBlockList[iterations - itMin]);
                        //test[iterations - itMin]++;
                    }
                    blocks.setBlock(vec, blocktype);
                }
            }
        }
    }
    context.print("Placed "+volume+" blocks!");
}

// the coordinate transform function
// returns a number between -1 and 1
function tf(v) {
    return (tfMult * v)/d - tfSub;
}

// vector magnitude function
// returns the length of the vector
function mag(vec) {
    var x = vec.getX(), y = vec.getY(), z = vec.getZ();
    return Math.sqrt(x * x + y * y + z * z);
}

// vector addition function
// adds two vectors together
function add(v1, v2) {
    var x1 = v1.getX(), y1 = v1.getY(), z1 = v1.getZ();
    var x2 = v2.getX(), y2 = v2.getY(), z2 = v2.getZ();
    var output = new Vector(
        x1+x2, 
        y1+y2, 
        z1+z2);
    
    return output;
}

// vector growth formula
// if current vector magnitude > 1 and t is not too close to a multiple of (pi/2)
// this will give a vector of greater magnitude than the vector put in
// n, which is param, is the rate at which vector magnitude grows.
function formula(vec, n) {
    var t = theta(vec);
    var p = phi(vec);
    var k = Math.pow(mag(vec), n);
    var output = new Vector(
        k*Math.sin(n*t)*Math.cos(n*p), 
        k*Math.sin(n*t)*Math.sin(n*p), 
        k*Math.cos(n*t));
    
    return output;
}

// theta vector value (arccos)
function theta(vec) {
    var x = vec.getX(), y = vec.getY(), z = vec.getZ();
    return (Math.acos(z/(mag(vec) + thetaAdj)));
}

// phi vector value (arctan)
function phi(vec) {
    var x = vec.getX(), y = vec.getY(), z = vec.getZ();
    return (Math.atan(y/(x + phiAdj)));
}

// distance from center
// moves vector origin to center and calculates its magnitude
function rfc(x, y, z) {
    var vec = new Vector(x - (d/2), y - (d/2), z - (d/2));
    return mag(vec); 
}

the third iteration yields 
331176/1000000 = 33.1176% of the volume

fourth iteration yields 
212260/1000000 = 21.2260% of the volume

fifth iteration yields
59761/1000000 = 5.9761% of the volume

sixth iteration yields
27566/1000000 = 2.7566% of the volume

seventh iteration yields
14745/1000000 = 1.4745% of the volume

eight iteration yields 
10010/1000000 = 1.0010% of the volume

ninth iteration yields
6521/1000000 = 0.6521% of the volume

tenth iteration yields
5447/1000000 = 0.5447% of the volume

eleventh iteration yields
4015/1000000 = 0.4015% of the volume

twelfth iteration yields
3294/1000000 = 0.3294% of the volume

thirteenth iteration yields
2587/1000000 = 0.2587% of the volume

fourteenth iteration yields
2540/1000000 = 0.2540% of the volume

fifteenth iteration yields
2058/1000000 = 0.2058% of the volume

the tenth-fifteenth iterations account for only 1.99% of the volume (higher iterations would account for an even lower % of the total volume.