Papers & Articles
A proposal for a Fractal Catalog
This article proposes the creation of an Online Encyclopedia of Fractals (OEF), a comprehensive, standardized repository for cataloging the infinite diversity of fractal geometries. The OEF would utilize a novel, line-oriented domain-specific language called Fracta to encode fractal generation algorithms in a compact, human-readable format. The article also addresses the challenges of duplicate detection and mathematical mimicry in fractal classification, proposing automated visual fingerprinting and empirical dimension estimation techniques to ensure a clean, non-redundant database.
The Cell Bar Chart: A Density-Aware Overlay for Bivariate Data
This article introduces the Cell Bar Chart, a bivariate visualization method that combines scatter-level fidelity with explicit local density encoding. The method overlays vertical density bars onto a scatter field to mitigate overplotting while preserving point-level interpretation. We present the visual rationale, algorithmic formulation, implementation details, practical tuning guidelines, and known limitations.
Symbolic Synthesis of Eulers Number and the Golden Ratio
This paper analyzes the structural configurations generated by symbolic regression driven by genetic algorithms (GAs) when tasked with approximating or defining fundamental mathematical constants ($e$ and $\Phi$). Unbound by human design heuristics—such as the classical preference for visual symmetry and algebraic parsimony—the evolutionary process yields unconventional functional architectures. We examine the mechanics of asymptotic convergence, the automated leveraging of removable singularities, and the algebraic invariance of the evolved continued fractions.
Fracta Language Specification: A Deterministic Syntax for Fractal
This document defines the formal grammar, lexical structure, and runtime execution semantics of Fracta v1.0, a minimalistic, line-oriented domain-specific language (DSL) designed for the generation of recursive geometric topologies. Fracta maps string-rewriting Lindenmayer Systems (L-Systems) directly into deterministic vector trajectories via a stack-based turtle graphics state machine. The language optimizes syntactic overhead to achieve low cognitive friction and high parse efficiency in resource-constrained or distributed environments.
Online Encyclopedia of Fractals (OEF) Standard
This document specifies the Data Schema, Meta-syntax, and Execution Core for the Online Encyclopedia of Fractals (OEF) alongside its accompanying Domain-Specific Language, Fracta. OEF provides a plaintext, peer-submittable registry for mathematical fractals, architectural structures, and chaotic systems. It addresses the structural equivalence challenge (where disparate algorithmic generators produce identical geometric attractors) by indexing topologies via an automated box-counting Hausdorff dimension algorithm combined with a discrete, coordinate-normalized Jaccard intersection engine. This enables algorithmic duplicate prevention, deterministic cataloging, and the automatic classification of mathematical anomalies.
Data Sheet Structure (DSS) Specification Version 1.0
This document specifies the Data Sheet Structure (DSS) version 1.0, an application-layer, plain-text data serialization format optimized for representing multi-sheet, sparse tabular datasets. DSS is designed to maintain native human readability and maximize compatibility with line-oriented version control systems (e.g., Git) by eliminating arbitrary formatting padding and treating spreadsheets as a collection of coordinate-mapped data matrices.