Runs
0
Extend the Collatz idea to any modulus and any operation. Pick a modulus m, then assign a different mathematical operation to each residue class — linear maps, powers, roots, logarithms, exponentials, polynomial derivatives, integrals, rational functions, and more. Stack runs, watch trajectories cascade, and inspect every step.
Set a start value, build and overlay runs. The rule system below defines what happens at each step.
Choose a modulus m. For each residue class r = 0, 1, …, m−1, assign an operation. At each step, compute n mod m to pick a rule, then apply it to get the next n. All residues are always covered — no gaps.
Each run starts at your chosen n₀ and applies your rule system repeatedly. At every step, n mod m selects one of your residue rules, which applies its operation to produce the next n.
Multiple overlay runs let you compare trajectory shapes, peak behaviors, and convergence. Use mod 2 with divide for residue 0 and linear 3n+1 for residue 1 to get classic Collatz.
Try exotic rules: mod 3 with power, root, and log operations — then watch for cycles, divergence, or surprising convergence. The on-canvas HUD shows the live calculation at every step of the active run.
Click any row in Overlay Runs to inspect the full step-by-step sequence with calculations.
0
0
0
0
0
0
-
-