Vertices 6
Edges 6
Genus 1
deg(D) 0
Selected 0
positive
zero
debt
Chip-firing preserves deg(D).
Graph
Preset
— select —
6-cycle (A–F)
Tetrahedron (K₄)
Cube
Octahedron (K₂,₂,₂)
Dodecahedron
Icosahedron
Complete graph Kₙ
Chain of cycles
n =
Cycle lengths:
Load
│
Import JSON
Export JSON
Mode
Select
Pan
Build
Fit view
│
Undo
│
Selected
+1 chip
−1 chip
Fire
Borrow
│
Divisor
Zero
Canonical
│
Dhar
Burn from selected
Clear burn
Select one or more starting vertices
This simulator requires JavaScript.
Controls
Modes
Select mode Click a vertex, or box-drag to select several; selection persists until you change it
Pan mode Drag canvas to pan; drag vertices to reposition
Build mode Double-click canvas to add vertex; Shift-drag vertex→vertex to add edge; right-click vertex or edge to delete
Mouse wheel / pinch Zoom in every mode, centered on the pointer or gesture
Chip-firing
Double-click vertex Fire that vertex (send one chip along each edge)
Shift + double-click vertex Borrow at that vertex (pull one chip from each neighbor)
Select + Enter / Fire Selected Fire all selected vertices simultaneously
Shift + Enter / Borrow Selected Borrow at all selected vertices simultaneously
+1 / −1 chip Change every selected vertex; works well on touch screens
Right-click vertex Context menu: add / remove / set chips (Pan & Select modes)
Zero Divisor Set all vertices to 0 chips
Canonical Divisor Set each vertex to deg(v) − 2
Undo Undo last chip or graph change (all operations supported)
Dhar's burning algorithm
Select vertices + B / Burn Start the fire from every selected vertex; a single starting vertex also tests whether the divisor is q-reduced. When the burn stops, the unburnt vertices become the selected set
Clear Burn Remove burn animation and highlighting
JSON import / export
Divisor convention. Firing is always allowed here, even when a vertex has fewer chips than its degree; negative values record debt. The total degree of the divisor is invariant.
JSON format compatible with Graph / Finite State Machine Designer (GFSM Designer) .
JSON
Graph JSON
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