PTI: A Hierarchical Symbolic Color Addressing System
2026-08-03 • Graphics
Graphics
AI summaryⓘ
The authors present PTI, a method to represent digital colors using a special code based on dividing the RGB color space repeatedly into smaller parts. Unlike usual methods that forget the path taken during this division, PTI keeps this path as a unique sequence that completely identifies the color without losing any detail. This sequence corresponds to a series of digits showing choices made in each subdivision step, making it easy to understand how a color relates to others hierarchically. PTI's coding is closely related to known techniques like Morton codes and octree quantization but focuses on maintaining a clear structure that can help in organizing colors and creating new palettes within standard RGB space.
RGB color cubeHierarchical color processingOctree quantizationMorton codeRecursive binary subdivisionColor addressingSymbolic identifierColor palette generationHierarchical interpretationPrefix semantics
Authors
Hector M. Trevino
Abstract
This paper introduces PTI (Persistent Traversal Identity), a hierarchical symbolic addressing system for digital color derived from the recursive binary subdivision of the RGB color cube. Standard hierarchical color processing systems organize colors via recursive space partitioning but conventionally discard the traversal path once computation is complete. PTI formalizes the preservation of that traversal path as a persistent symbolic identifier. The resulting address is a finite sequence of eight-valued digits from the set {0, ..., 7}, each encoding the octant selected at one level of subdivision. Concatenated, they constitute a lossless alternative representation of any 8-bit-per-channel RGB color. PTI is structurally equivalent to the Morton (Z-order) code of a color interpreted as a sequence rather than an integer, and its construction algorithm is the octree traversal procedure of classical octree quantization, as established by Gervautz and Purgathofer. PTI does not introduce a new color space, nor does it claim to improve upon these foundational methods. Its contribution is a color representation that is simultaneously machine-precise and hierarchically interpretable, revealing a color's family lineage directly from its address structure. The same 8-digit address decodes losslessly to RGB and reads compositionally as a named sequence of weighted color directions. PTI's well-defined prefix semantics support direct address operations suited to color catalog organization, truncation-based image-processing routines, and structured exploration of colors. The address structure invites further operations beyond this. A simple one, successively rotating the address by one digit position, creates structurally harmonious color palettes derived directly from the geometry of the RGB cube, never leaving RGB.