Slim Fractals

Scale-dependent fractals whose fractal dimension decreases with resolution; the paper finds EqR-Sudoku basins exhibit this signature.

Neighborhood — ranked by edge-count

paper

thinker

Adilson E. Motter
introduces
Characterized 'slim fractals' (scale-dependent fractal dimension), the concept the paper uses to classify EqR-Sudoku basins.

concept

Fractal Basins
associated_with
Self-similar convergence-time basins the paper finds in reasoning models' latent initial-condition space, growing with task difficulty.

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

Slim fractals (scale-dependent fractal dimension) arise in physical systems with dissipation, where the saddle-like set decays over timeclaim0.790
Explains why EqR-Sudoku basins show decreasing fractal dimension with zoom.
fractal geometryconcept0.758
Mandelbrot's framework for describing self-similar and scale-invariant structures; cited as a possible theory for the void.
Wholenessconcept0.698
Alexander's core concept rejecting the idea that a whole consists of parts; instead, a whole makes its parts (called 'centers').
larger wholesconcept0.692
The broader field of centers that encompasses a given center; a successful center contributes to and is shaped by these larger wholes.
Physical Materials, Shapes, and Phenomenaconcept0.676
Fraternal Transitionconcept0.675
ETI where HFHF is solved by phenotypic plasticity and homogeneous genetics; e.g., multicellularity with genetically identical cells
Multiscale systemsconcept0.670
Systems prevalent in biology that can organize into complex patterns; architecture supports long-range coherence.
Gradientsconcept0.670
The property that qualities vary slowly, subtly, gradually across the extent of each living thing; gradients arise as natural responses to changing circumstances and create field-like character that points toward and establishes centers