Information
Enter a starting value and click Generate to visualize its Collatz trajectory. Click on any lattice point or use keyboard navigation (n/p) to see its trajectory.
Legend:
Keyboard Controls:
- n - Next point in trajectory
- p - Previous point in trajectory
- Shift+N - Jump to next circuit
- Shift+P - Jump to previous circuit
- s - Toggle animation
Formulas:
A(n,x) =
- 3·2n-1 + 2n+1·x - 1, if n odd
- 2n-1 + 2n+1·x - 1, if n even
B(n,x) =
- 3·2n + 2n+2·x - 1, if n odd
- 2n + 2n+2·x - 1, if n even
C(n,x) = 2·3n·x + 4·Σi=0⌊(n-1)/2⌋ 9i
About:
This visualization shows the (n,x) lattice where each point represents values from the branch formulas A(n,x) and B(n,x). These formulas classify odd integers by their Steiner circuit structure in the Collatz map.
The lattice displays n on the x-axis and x on the y-axis (with logarithmic scale), since x can be large while n typically stays small.
Points marked - correspond to A(n,x), while points marked + correspond to B(n,x). Both branches at a given (n,x) map to the same endpoint C(n,x).
The wave visualization shows the selected node in green with larger radius, while successors appear in blue and predecessors in red, with intensity and size decreasing with distance from the selected node.