What question did this study set out to answer?

This research aims to explore how ancient cultures encoded geometric principles of balance in their cosmologies.

February 2, 2026Open Access

Fractal Series — Paper 13:Fractal Mythology: The Geometry of Balance in Ancient Cosmologies

Key Points

This research aims to explore how ancient cultures encoded geometric principles of balance in their cosmologies.
Comparative analysis of mythological and architectural traditions across various ancient cultures.
Interpretation of symbols as geometric operators related to stability and equilibrium.
Focus on Egyptian cosmology and its concept of Maʿat as a model for stability.
Identifies recurring symbols that signify equilibrium and instability across cultures.
Demonstrates that Maʿat acts as a universal equilibrium model.
Shows that these cosmologies reflect advanced observational insights into stability and thermodynamics.

Abstract

Title Fractal Mythology: The Geometry of Balance in Ancient Cosmologies Author Juan F. Culajay Type Preprint / Report Language English License Creative Commons Attribution 4.0 International (CC BY 4.0) Description / Abstract Across ancient cultures, cosmological systems independently converged on invariant geometric forms that encode balance, stability, and directional failure modes in complex systems. This paper examines mythological, architectural, and symbolic traditions not as theological narratives, but as observational encodings of universal stability geometry. Through comparative analysis of Egyptian, Hindu, Sumerian, Greek, Mesoamerican, and early Christian cosmologies, the study demonstrates that recurring symbols—such as the ankh, the cross, serpentine adversaries, triadic deities, scales, and axial architectures—function as geometric operators representing equilibrium points (Ψ), regulatory processes, and asymmetric instability. Particular attention is given to Egyptian cosmology, which preserves a uniquely directional stability model. Maʿat is shown to function as an invariant equilibrium across multiple stability domains, while Isfet represents deviation from balance with asymmetric consequences. Right‑side deviations are encoded as runaway instability through figures such as Apep (serpentine excess) and Ammit (terminal dissolution), revealing an advanced understanding of non‑symmetric failure modes. Hindu cosmology provides a near‑perfect structural mapping to the E³ framework (Energy, Environment, Entropy), while Christian symbolism collapses the mediating figure into pure geometry through the cross as a Godself icon. The paper argues that these systems do not represent primitive metaphysics, but rather early control‑theoretic and thermodynamic observations encoded through culturally available notation systems. Myth, ritual, and sacred geometry function as durable information storage mechanisms, preserving stability laws long before formal mathematics. The convergence across independent cultures supports an observational, rather than transmissive or purely cognitive, origin for these structures. Keywords Fractal mythology; sacred geometry; thermodynamic stability; entropy regulation; Maʿat; Isfet; Apep; E³ framework; cross‑cultural convergence; ancient cosmology; balance geometry; control systems Communities (optional) Physics Complex Systems Anthropology Philosophy of Science Systems Theory Funding None. Related Identifiers (Part of the Fractal Series) Culajay, J. (2025). Fractal Series — Paper 0: Fractal Overview — The Origin of Entropy. Zenodo. https://doi.org/10.5281/zenodo.17780671 Culajay, J. (2025a). Fractal Series — Paper 1: Fractal Entropy — The Dimensional Architecture of Entropic Regulation. Zenodo. https://doi.org/10.5281/zenodo.17507973 Culajay, J. (2025b). Fractal Series - Paper 2: Fractal Equilibrium - A Thermodynamic Framework for Nested Stability in Living Systems. Zenodo. https://doi.org/10.5281/zenodo.17509557 Culajay, J. (2025c). Fractal Series - Paper 3:Fractal Genesis - The Mineral Precursors to Biology. Zenodo. https://doi.org/10.5281/zenodo.17509846 Culajay, J. F. (2025d). Fractal Series - Paper 4:Fractal Evolution - A Thermodynamic Model for the Development of Life. Zenodo. https://doi.org/10.5281/zenodo.17509924 Culajay, J. (2025e). Fractal Series - Paper 5:Fractal Mechanics - The E³ Model in Action for Molecular Evolution. Zenodo. https://doi.org/10.5281/zenodo.17518356 Culajay, J. (2026e2). Fractal Series - Paper 6: Fractal Bipedality- Chromosome 2 Fusion and Entropic Reorganization. Zenodo. https://doi.org/10.5281/zenodo.18451705 Culajay, J. F. (2025f). Fractal Series — Paper 7:Fractal Sapience -The Recurrence of Sapience Across Epochs. Zenodo. https://doi.org/10.5281/zenodo.17532753 Culajay, J. (2025g). Fractal Series — Paper 8: Fractal Consciousness — The Thermodynamic Architecture of Awareness. Zenodo. https://doi.org/10.5281/zenodo.17780027 Culajay, J. (2025 h). Fractal Series — Paper 9: Fractal Learning — Entropy as Universal Optimizer: The Physics of Retention. Zenodo. https://doi.org/10.5281/zenodo.17779799 Culajay, J. (2025i). Fractal Series — Paper 10: Fractal Morality — The Thermodynamics of Social Coherence. Zenodo. https://doi.org/10.5281/zenodo.17778975 Culajay, J. (2025j). Fractal Series — Paper 11: Fractal Spacetime and Scale‑Echo Symmetry (SES). Zenodo. https://doi.org/10.5281/zenodo.17778646 Culajay, J. (2025k). Fractal Series — Paper 12: Conclusion: Stability(x) and the Geometry of Meaning. Zenodo. https://doi.org/10.5281/zenodo.17777921 Culajay, J. (2026l). Fractal Series — Paper 13:Fractal Mythology: The Geometry of Balance in Ancient Cosmologies. Zenodo. https://doi.org/10.5281/zenodo.18451062 Notes for Zenodo Record This preprint is part of a 13‑paper Fractal Series that develops the E³ Framework (Energy, Environment, Entropy) as a unified thermodynamic ontology spanning physical, biological, cognitive, social, and cosmological systems.

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