What does this visualization show?

This graphic illustrates the jumps of the Collatz sequence (3n+1) for a specific range of starting numbers. The numbers are arranged along the circumference of a circle:

One half of the circle: Here you find our odd starting numbers (from 1 to 2^B-1).
The other half of the circle: This is where the numbers reached during the sequences land. Since the values can grow extremely large due to the 3n+1 operation, this area is structured according to the bit length of the numbers (up to 3B-1).
The orange dots: These dots mark all odd multiples of 3 (3, 9, 15, 21...) on the entire circle. They reveal a central secret of the Collatz problem: A 3n+1 operation (followed by halving) can never produce a multiple of 3. Thus, these numbers are never 'landed on'. They are purely starting points, which is why they must be 'brought' into the starting half to see their paths at all.
The paths (lines): Each arc represents one step within the sequence. Using the input field, you can highlight the path of a specific starting number in red to track exactly how it wanders through the dimensions of the circle.

Accordion