The Quantized Blueprint of Odd Integers
For six instruments, we have tracked the chaotic dynamics of the Collatz trajectories—measuring their peaks, glides, and lifespans (App 6). Now, we look beneath the motion to reveal the structure.
The Collatz Atomic Model moves beyond analyzing behavior to visualize anatomy. Drawing a direct parallel to quantum mechanics, it reveals that odd integers do not exist in a disorganized heap. Instead, they occupy precise, discrete “Energy Shells” (labeled K, L, M, N, O) based on their fundamental arithmetic properties (“Crash Power” r).
This is the static map of the Collatz universe—the highly organized skeleton upon which the chaotic dynamics play out. For the documentation about different numbers refer to the blog on Collatz atomic model in my website.