Symmetry-aware
Neural interestingness #1
X59379_M3
ETC center X(59379); M3 = pedal triangle; the center is reevaluated at every iteration.
Triangle-space dynamics · interactive research atlas
Beauty of
Triangle Centers
Fractal attractors produced by repeatedly rebuilding a triangle from one of its centers - seen not in the Euclidean plane, but in the barycentric space of all triangle shapes.
72,807ETC centers searched
145,614M1 and M3 candidate maps
1,847taste-selected diagrams
360ranked atlas positions
Three-way equal-rank comparison
Three ways of finding visual structure
At every position, the neural interestingness result is paired with the same-ranked raw quadtree code-length result and the same-ranked modified-compressibility result. Raw quadtree code bits are ordered from lowest to highest. The modified measure is the former Wundt gate, 4q(1−q), ordered from highest to lowest.
Raw spatial compression
Compressibility #1
X31498_M1
ETC center X(31498); M1 = cevian triangle; the center is reevaluated at every iteration.
Complexity moderated
Modified compressibility #1
X31498_M1
ETC center X(31498); M1 = cevian triangle; the center is reevaluated at every iteration.
Optional visual-preference study
What is aesthetically more pleasing: interestingness (left), compressibility (middle), or modified compressibility (right)?
Rank all three pictures from most to least pleasing. Your choices are saved in this browser, can be revised, and are summarized below.
Your preferences
Your emerging aesthetic profile
Scores and global ranks use the completed 20,000-point analysis. Display images normally use 50,000 retained points after 4,000 discarded iterations and all six angle permutations; finite orbits use their longest valid prefix. The middle diagram is visually inverted for the triangular comparison and this presentation is recorded with every submitted ranking. PNG downloads retain the original complete canvas. Use the left and right arrow keys to change rank.
From 145,614 maps to an atlas
A computational search, guided by taste
The catalogue is a selection rather than an assertion that beauty has a single numerical definition. Automatic filters removed failed, degenerate, and strongly rejected diagrams; a fitted personal-taste model then supplied a fixed threshold for the full ETC search.
Iterate the geometry
For every ETC center, M1 replaces a triangle by its cevian triangle and M3 by its pedal triangle. The center is recomputed after every step.
Learn what survives
A rejection model and a personal preference model were trained from visual judgments. The final catalogue retained 1,847 center-map records.
Measure discoverable structure
Neural learning progress estimates how much hidden structure an observer can discover. Quadtree and PNG ratios provide explicitly spatial compression measures.
Compare equal ranks
The web atlas presents equal positions from neural interestingness, ascending raw quadtree code bits, and the former Wundt-gated modification without recomputing their scores.
Two compression orderings
Raw compressibility is ranked by ascending quadtree code bits. Modified compressibility uses 4q(1−q), where q is the quadtree code length relative to an equal-density random raster, and is ranked descending.
Complete publications
Read and download the atlases
Both source atlases are preserved as complete PDF files. Preview them in the browser or download an unmodified copy.
01
95 pages · 47 triangle centers
Common-47 Triangle-Center Dynamics Atlas
A broad dynamics atlas covering eight iterated words, interestingness, fractal dimensions, mathematical importance, and fitted personal taste.
02
120 A3 pages · 360 ranked positions
Three Triangle Compressibility and Interestingness Atlas
Every page compares equal positions from neural interestingness, ascending raw quadtree code bits, and modified compressibility. The middle diagram is visually inverted and enlarged between the two upright diagrams.