Radial Visualization of Collatz Stopping Times: Emergent 8-fold Symmetry

This dataset presents a radial visualization of the stopping times in the Collatz ("3x+1") problem for integers from 1 up to 100,000.

Each wedge corresponds to an integer, ordered sequentially in polar coordinates.

The brightness of each wedge is mapped to the number of steps required for that integer to reach 1 under the Collatz iteration:

Brighter wedges represent integers with shorter stopping times.

Darker wedges indicate longer stopping times.

Remarkably, the resulting structure exhibits a clear 8-fold rotational symmetry, reflecting deep modular patterns related to the binary structure of integers modulo 8.

This visualization highlights hidden regularities in the distribution of stopping times and suggests a profound 2-adic modular organization underlying the Collatz dynamics.

Additionally, wedge-based visualizations for n=1 to 1024, 8192, and 16384 are available for comparison:
https://imgur.com/a/collatz-3-Edx5TD4