Collatz stopping times

O(n · k)

The Collatz conjecture (unsolved since 1937) states that repeatedly applying the map m→m/2 (even) or m→3m+1 (odd) always eventually reaches 1. The total stopping time — the number of steps to reach 1 — varies wildly and has no known closed form. This visualiser computes the stopping time for each m in 2..n and assigns it to a colour band: tan for ≤10 steps, amber for 11–20 steps, and green for >20 steps, producing a striking heatmap. The cell labels show the exact step count.

Numbers
Edit the input and press Play

How it works

  1. Initialize all cells 2..n as candidates
  2. For each m compute its Collatz stopping time
  3. Assign colour band: ≤10 tan, 11–20 amber, >20 green
  4. Label each cell with its step count

Pseudocode

1collatzSteps(m):                    # steps to reach 12  steps = 03  while m != 1:4    m = m/2 if even else 3*m + 15    steps += 16  return steps78collatzGrid(n):                     # O(n * k)9  for m = 2 to n:10    s = collatzSteps(m)11    band[m] = "low" if s<=10 else "mid" if s<=20 else "high"