File talk:Collatz-tree, depth=20.svg
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Shades of grey for number of binary ones?
[編集]Suggestion: Fill the ellipses with a shade of grey based on number of binary ones
- light grey: 1, 2, 4, 8, ... all with (1)
- intermediate shades of grey: (2) - (9)
- dark grey: for 349525 (10)
What it will show is some order, not the very chaotic "hailstone sequence" shown by other graphs:
- most numbers flow from many (dark grey) via intermediate shades towards 1 (light grey) binary one.
- giant leaps are exceptional, e.g. 349525 (10) to 1048576 (1)
- some sequences stay within the same shade of grey for some time, e.g. 8832, 4416, 2208, 1104, 552, 276, 138, 69, 208 104, 52, 26, 13, all (3).
- reverse direction is possible, but rare, such as 35 (3) -> 106 (4)
The graph as a whole will illustrate that the Collatz conjecture is probably true, yet not proven. Uwappa (トーク) 13:25, 25 June 2024 (UTC)