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Part B: The Swirling Gases

Note: Before diving in, check out Part A: The Smoke Pillar for context.

This guide lays out the mathematical setup for creating a mushroom cloud. Let’s get swirling.

A mushroom cloud consists of two main parts:

This page is all about Part B; the swirly gas vortex thingy.

Math Time

WARNING: High levels of BS trig and circle math ahead. You have been warned.

Alright, time to model the swirly gases. Here’s a diagram to visualize what we’re dealing with:

We use sine and cosine to calculate how much each particle moves. And since describing math with words alone is painful, here’s more diagrams. Hooray!

By shifting a particle by (sin(angle), cos(angle)) as angle increases, we get a loop. At first, it looks more like a square than a circle, but don’t panic, we can just decrease the angle increment. Also, if you’re wondering why X is offset by sin and Y by cos (instead of the usual way), it’s so the particles move outward and then back in, meeting at a single point (which we can later tweak into a torus!).

Here’s what different increment values look like. Each set has one less visible point than labeled due to the 0→2π loop. More points = smoother circle. In Minecraft, if you call super.tick() before displacement, it smooths out movement, so even Set 2 will look like it has way more than 10 points. Also, the more points you add, the bigger the circle gets. This happens because P' = P + (sin(angle), cos(angle)), and a smaller increment moves P' farther. You could "fix" this with ratios or something fancy, but honestly, just test it in-game. Too big? Divide the displacement value. Too small? Multiply it. Math is constant, but art is a process. You’ll have to tweak things. I highly recommend adding dev commands to adjust radius values live in-game, it'll save you from the dreaded 'Close Game -> Change Variable -> Open Game -> Test -> Repeat'.

Now this is a lot of confusing math, so if you learn by example or by good ol' copy-paste, here you go:


public void partB() {
    swirlAngle += swirlIncrement;
    if (swirlAngle >= 2 * Math.PI) swirlAngle -= 2 * Math.PI;

    float rStart, rEnd, gStart, gEnd, bStart, bEnd;
    if (swirlAngle < Math.PI) {
        rStart = 255; rEnd = 115;
        gStart = 75; gEnd = 115;
        bStart = 0; bEnd = 115;
    } else {
        rStart = 125; rEnd = 255;
        gStart = 115; gEnd = 75;
        bStart = 115; bEnd = 0;
    }
    float progress = (float) ((swirlAngle % Math.PI) / Math.PI);
    this.rCol = Math2.interpolateColor(rStart,rEnd,progress);
    this.gCol = Math2.interpolateColor(gStart,gEnd,progress);
    this.bCol = Math2.interpolateColor(bStart,bEnd,progress);

    double verticalMovement = Math.cos(swirlAngle) * swirlRadius;
    double horizontalMovement = Math.sin(swirlAngle) * swirlRadius * 1.5;
    localY += verticalMovement;
    localZ += horizontalMovement;
    double relativeX = localX - originX;
    double relativeY = localY - originY;
    double relativeZ = localZ - originZ;

    Vector2D rotatedXZ = Math2.rotateCoordinate2D(relativeX, relativeZ, rotationAngle).offset(offsetX, offsetZ).offset(originX, originZ);
    this.setPos(rotatedXZ.x, originY + relativeY, rotatedXZ.y);
}