This repository contains the official computational framework and MATLAB implementation for rendering 3D modular surface visualizations of holomorphic functions, as presented in my research paper.
This project synthesizes the analytical mechanics and geometric topographies of complex function mappings. By investigating holomorphic transformations through the geometric lens of Tristan Needham's "Amplitwist" framework, these scripts computationally verify coordinate orthogonality and map functional magnitude as spatial height, using phase arguments as a continuous color spectrum.
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Specimen A - Exponential Mapping:
$e^z$ (Transcendental family) -
Specimen B - Reciprocal Inversion:
$1/z$ (Rational family) -
Specimen C - Periodic Sine:
$\sin(z)$ (Trigonometric family)
- MATLAB (R2020a or later recommended)
- Symbolic Math Toolbox (Optional, for running analytical checks)
- Clone this repository:
git clone https://github.com/saurinshah14/Complex-Conformal-Mappings---Amplitwist-in-3D-Modular-Surfaces.git - Open MATLAB and navigate to the
scripts/directory. - Run any specimen script (e.g.,
SpecimenA_3DModularSurface.m) to generate the interactive 3D modular surface meshes.
If you use this code or the associated analytical framework in your research, please cite the preprint: Saurin Jitendra Shah, "A Unified Framework for Complex Analysis and Spatial Geometry: Bridging Cauchy-Riemann Mechanics, the Amplitwist, and 3D Modular Surface Visualizations," Zenodo Preprint, 2026. DOI: 10.5281/zenodo.21261115