Core Principle

Natural systems exhibit fractal recursion: patterns repeat across scales via feedback and self-similar constraints. The E³ model treats:

  • Energy — driver of motion, reaction, and transformation.
  • Environment — boundary conditions that shape possible configurations.
  • Entropy — equilibrating process that redistributes energy toward steady states.

Entropy here is modeled as a harmonizing process, not mere disorder.

Foundational Assertions

  • Fractal Recursion: energy flows and forms follow scale-free, self-similar patterns (e.g., branching, networks, power-law scaling).
  • Nested Steady States: stability emerges through layered equilibria (cell → tissue → organism → ecosystem).
  • Entropy as Equilibrator: systemic balance arises via energy redistribution, enabling both order and diversity.
  • Emergence via Feedback: adaptation and complexity result from recursive E↔Env interactions under entropy constraints.

The Structure of the Fractalism Series

Peer-review–ready • Science only
Paper Domain Scientific Focus
Fractal Entropy Thermodynamics Reframes entropy as a harmonizing process driving systems toward equilibrium. Shows how entropy structures order and complexity in physical and biological systems.
Fractal Equilibrium Systems Physics Analyzes dynamic balance in open systems. Defines nested equilibria as the thermodynamic architecture of life under continuous energy flow and entropy exchange.
Fractal Genesis Prebiotic Chemistry Explores how self-organization arises from recursive energy–entropy cycles in mineral/aqueous environments; establishes minimal E³ conditions for proto-metabolism.
Fractal Evolution Biology Models evolution as recursive feedback between energy flow and environmental constraint; explains scaling of adaptation, replication, and complexity.
Fractal Mechanics Molecular Biophysics Shows molecular machines (ATP synthase, ribosome, ion channels) as fractal steady states optimizing E–S efficiency under environmental constraints.
Fractal Sapience Cognitive Biology Defines sapience as an emergent thermodynamic attractor recurring when E³ alignment crosses complexity thresholds in evolutionary lineages.
Fractal Consciousness Neurophysics & Systems Theory Models awareness as recursive informational geometry (feedback equilibria) across brain networks with scale-free topology.
Fractal Morality Behavioral Science Frames cooperative/competitive behavior as entropy-regulating dynamics that minimize systemic conflict and sustain long-term equilibrium.
Fractal Spacetime Theoretical Physics Extends E³ to cosmology; investigates whether spacetime geometry and quantum/relativistic phenomena reflect recursive energy–entropy harmonization.

Phase map: Entropy → Equilibrium → Genesis (thermodynamic foundation) → Evolution → Mechanics → Sapience (biological application) → Consciousness → Morality → Spacetime (systemic extension).

Objectives

  • Unify physics, biology, and cognition with one mathematical language of recursion.
  • Model life and evolution as thermodynamic processes — not exceptions to them.
  • Reinterpret entropy as the organizing principle behind stability, diversity, and growth.
  • Provide predictive tools for emergent complexity across domains.

Working Definition

Fractalism is the study of how recursive Energy–Environment–Entropy interactions produce self-similar structure, stability, and adaptive complexity across scales.

Selected Research Applications

  • Molecular Biology: protein folding, self-assembly, and nano-machines as E–S optimizers.
  • Ecology: population/resource dynamics as nested equilibria under energy flux.
  • Neuroscience: scale-free brain networks and feedback equilibria of cognition.
  • Astrobiology: thermodynamic criteria for life’s emergence in non-terrestrial environments.
  • Physics: fractal spacetime hypotheses linking quantum behavior and macroscopic order.
  • Computation: recursive algorithms to simulate E³ dynamics.