Gravity Maps

Abstract

Gravity Maps are a newly discovered class of integer mappings that generalise the well-known Collatz function. Defined through simple modular rules, these mappings extend beyond a single base and exhibit consistent collapse of trajectories to unity. While no formal proofs are attempted here, empirical exploration reveals striking properties, particularly in the Efficient Version: odd and even subsequences form strictly decreasing sequences and trajectory lengths remain bounded - with a maximum of only 60 steps observed up to one billion. This work introduces the definitions of Gravity Maps, highlights their distinctive behaviour, and provides a platform for further study.