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Collatz Cascade Explorer

Pick a start value, build runs, and watch each trajectory cascade step-by-step.

Run Controls

Use the quick controls, then open the dropdowns only when you want deeper settings.

What happens each step: if n mod m = 0, we divide by d. Otherwise we apply a*n + b. You can use expressions with n and ^ (for example: 2n+1, n^2, (n+1)/2).

Rule Setup (Piecewise Function)

Divisible Branch

If n satisfies the modulus check, divide by d. m and d can be expressions in n.

Otherwise Branch

If not divisible, apply affine map a*n + b. a and b can also be expressions in n.

Rule Preview

Safety and Performance

What Am I Looking At?

Each run starts at your chosen n0 and applies the rule repeatedly. A new point is drawn at every step.

When multiple runs are added, they stay overlaid so you can compare trajectory shape and peak behavior.

Use Run History by clicking a row in Overlay Runs to inspect every exact value.

Runs

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Distinct Nodes

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Distinct Edges

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Longest Steps

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Peak Value

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Active Frame

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Current Active Node

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Hover Node

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Overlay Runs