The Modular Formula Builder

What the Modular does

Most formulas are fixed equations. The Mandelbulb iterates z → z8 + c. You can't rearrange it.

The Modular formula is different. It's a node-based editor where you build the iteration loop yourself by chaining operations:

z → Rotate → BoxFold → Scale → z8 + c

The graph compiles to GLSL on the fly and replaces the formula shader. You're effectively designing your own fractal.

Getting there

Open the Formula dropdown and pick Modular. A Graph tab appears in the right dock — that's the editor. You're now seeing a default preset, typically a Mandelbulb built from component nodes.

The node palette

Utils

• Comment / Note — documentation blocks inside the graph
• Add C — adds the constant c term (Julia / Pixel mode switching)

Transforms

• Scale (Mult) / IFS Scale (Homothety) — resize space
• Rotate — rotate coordinate system
• Translate — shift space
• Modulo (Repeat) — tile space infinitely

Folds

Folds are the heart of most non-power fractals — they reflect space across planes.

• Amazing Fold, Abs (Mirror), Box Fold, Sphere Fold
• Plane Fold, Menger Fold, Sierpinski Fold

Fractals

• Mandelbulb — the classic power iteration as a node

Primitives

These write an SDF distance value that can override the iterative DE:

• Sphere, Box

Distortion

• Twist (Z), Bend (Y), Sine Wave

Combiners (CSG)

These take two inputs and merge them:

• Union, Subtract, Intersect, Smooth Union, Mix (Lerp)

Adding nodes — Ghost Insert mode

1. Pick a node type from the "Add:" dropdown or the right-click context menu
2. A ghost tooltip follows your mouse — cursor becomes a crosshair
3. Click on an existing connection (highlighted cyan) to insert the node between its neighbors; the edge splits automatically
4. Click on empty canvas to place the node freely at that point
5. Esc to cancel

CSG / Combiner nodes need two inputs, so they can't be edge-inserted — click empty canvas to drop one in, then wire inputs manually.

Wiring connections

• Drag from a node's bottom handle (output) to another's top handle (input)
• CSG nodes have two top handles — A (left) and B (right)
• The chain starts at Input Z and ends at Output Distance
• Right-click a connection to delete it
• Cycles are prevented — you can't wire a node's output back into its own chain

Per-node controls

• Enable/Disable checkbox — temporarily bypass a node without deleting it. The card dims.
• × button — delete the node and reconnect its chain automatically (for single-input nodes)
• Right-click header — context menu with delete + help

The two hidden-but-essential node features

Parameter binding (A–F)

Every slider on every node has a dropdown next to it. Set it to A, B, ..., F to link that parameter to the corresponding global slider. Now it's driven by the main Formula panel — and because global sliders are animatable, you can keyframe deep graph parameters from the Timeline.

Bound parameters display in cyan with a (→ ParamX) label. Pick "—" to clear the binding.

Logic / Condition (per-iteration firing)

Expand the Logic section at the bottom of any node. Enable it, then set:

• Interval — node fires every N iterations
• Starting Iteration — which iteration in the cycle to start on

Example: Interval 3, Start 1 → runs on iterations 1, 4, 7, 10, ... This is how you create layered hybrid fractals inside a single graph — folds that alternate with power iterations, transforms that only apply periodically.

Compile controls

• Auto Compile — recompiles the shader after every structural change. Convenient but slower to work with on big graphs.
• COMPILE — manual compile button. Pulses when changes are pending.
• Ctrl+Z / Ctrl+Y — undo/redo graph changes including node positions
• MiniMap — overview in the corner, color-coded by category

Load a preset to start

The "Load:" dropdown has pre-built chains as starting points:

• Mandelbulb (Standard), Amazing Box, MixPinski
• Menger Sponge, Kleinian, Marble Marcher

Start with one of these, tweak, and learn by modification. Much faster than building from scratch.

Exporting a Modular formula

Save a scene with the System Menu — GMT writes the compiled GLSL into the .gmf file, so anyone loading it gets your exact formula, not a re-resolved version of the graph.

If you want to share just the graph structure (not a rendered scene), the .gmf file still carries it — other users can open it in the Modular editor and continue modifying.

Where to go from here

The Modular is where GMT becomes a real tool for designing fractals, not just exploring them. It rewards experimentation — swap nodes, bind to sliders, animate. Most of the interesting shapes in the community have been discovered by people dragging nodes around and seeing what happens.