Collatz Matrix: The periodic table of Chaos

collatz matrix

This tool moves beyond simply calculating the Collatz sequence and attempts to classify it. Just as elements are organized in a Periodic Table, this matrix groups odd integers into families based on their behavior.

How to use this tool:

  • The Matrix Tab: Groups numbers by their “Crash Power” (r).
    • Rows (r): Show how many times the number divides by 2 immediately after growing.
    • Columns (m): Show the arithmetic family index.
    • Tip: Use the filters to isolate Odd Multiples of 3—the “orphan” numbers that can never be reached by other numbers.
  • The Plotter Tab: Allows you to map special number series onto the Collatz coordinates. Select Primes, Fibonacci, or Palindromes to see if they follow a pattern or scatter randomly across the chaos