Slim fractals (scale-dependent fractal dimension) arise in physical systems with dissipation, where the saddle-like set decays over time

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

• Slim Fractalsconcept0.790
  Scale-dependent fractals whose fractal dimension decreases with resolution; the paper finds EqR-Sudoku basins exhibit this signature.
• Levels of scale appear pervasively in natural systems such as trees, cells, rivers, mountain ranges, and galaxies.claim0.771
• Fractal basins and transient chaos are the generic manner in which computational complexity manifests in analogue systemsclaim0.760
  Generalizing interpretation connecting this paper's AI findings to physical analogue computation broadly.
• Levels of scale is not a mechanical thing requiring merely a wide range of sizes; it arises properly only when each center gives life to the next one and the detail actually does something to create life in larger centersclaim0.755
  Clarification that levels of scale fails when detail is merely present but not doing anything—as in machine-made doors with superficially many panels that have no real life
• Free-energy scaling under domain-wall formation in Potts, autoregressive, and hierarchical networks shows that combinatorics of interactions on a graph prevent or allow spontaneous ordering.finding0.747
  Core result demonstrating topological constraints on self-organization
• Even with non-linear dynamics and complexity theory, the specific appearance of the fifteen properties and emergence of living centers in the world remains largely unexplained.claim0.747
  Alexander's critical assessment of the limits of current complexity science relative to his explanatory target
• Multi-scale coherence may be the cause of aliveness, or only its signature—the causal direction remains open.claim0.746
• The kind of order that occurs in living structure has a complexity not usually describable by drawings or by architectural images.claim0.745
  Emphasizes the non-pictorial, process-dependent nature of living order.