Fractal image compression
Fractal image compression represents an image as a collection of contractive transformations that approximately map larger source blocks onto smaller target blocks.
Search for repeated structure
An encoder partitions the image into range blocks and searches domain blocks that resemble them after geometric and tonal transformation. The transformation list defines an operator whose fixed point approximates the original image.
The encoder divides an image into small range blocks and searches larger domain blocks that become similar after rotation, reflection, brightness and contrast adjustment. It stores transformation parameters rather than pixels. Strong matches require recurring local structure. The search is combinatorially large, so classifying and restricting candidates determines much of encoding cost.
Asymmetric cost
Decoding repeatedly applies the stored transformations and can start from many arbitrary images. Encoding is expensive because the search among block relationships is large; accelerating and constraining that search is central to practical systems.
Decoding repeatedly applies all transformations to an arbitrary starting image. Because the combined operator should be contractive, the sequence approaches its fixed point. This explains asymmetric cost: expensive relationship search during encoding and relatively simple iteration during decoding. Poorly conditioned or overly aggressive maps can harm convergence and image quality.
Zoom promises and practical tradeoffs
Because transformations define continuous mappings, decoded images can be evaluated beyond their original grid, but no missing photographic truth is recovered. Modern general-purpose codecs usually offer a better balance of speed, quality and support, leaving fractal compression historically important and specialized.
The transformations can be evaluated continuously, allowing a decoder to produce a larger raster. No additional photographic truth from the source is recovered; the model’s self-similarity assumption is refined. Modern codecs generally balance speed and quality better through block transforms, prediction and learned tools. Fractal compression remains conceptually important, not a universal route to lossless infinite zoom.
Sources and further reading
This article summarizes the following specialist sources in original wording. Accessed and editorially reviewed 12 August 2026.
- Fractal Image CompressionNotices of the American Mathematical Society
- Iterated Function SystemWolfram MathWorld
Continue the idea
Iterated function systems
How a small collection of contracting transformations defines a unique fractal attractor.
Fractal art: mathematics as material
How artists turn formulas, parameter search, color, texture, lighting and export decisions into authored images.
GPU fractal rendering
How fractal pixels use parallel Metal compute on Mac and Apple Silicon, where divergence and precision cost performance, and why progressive refinement matters.