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Research

GridMorph — Complex Grid Transformation

A MATLAB visualization of how the complex map w = z² + z warps a uniform spatial grid in real time.

Difficulty — intermediate Complexity — 4/10 Category — Research

Overview

A MATLAB simulation studying how the nonlinear complex function w = z² + z distorts a uniform rectangular grid — stretching, rotation and warping made directly visible, with every transformation manually cross-checked against hand-computed complex points.

Architecture

A grid-generation and complex-mapping engine that applies w = z² + z point-by-point across a uniform grid and renders the deformed result.

Key Features

  • Real-time visualization of grid deformation under a nonlinear complex map.
  • Manual computation of selected complex points cross-validated against MATLAB's mapped output.
  • Analysis connecting the visual distortion to real-world effects in signal transformation and physics simulation.

Development Process

  • Derived expected outputs for selected points by hand before running the full grid transformation.
  • Implemented the grid mapping in MATLAB and compared against the hand-derived values.
  • Built the visualization once numerical correctness was confirmed.

Challenges & Solutions

Challenge

Confirming the transformation was implemented correctly required more than a visually plausible plot.

Solution

Manually computed several complex points independently and cross-checked them against the MATLAB-generated grid before trusting the visualization.

Results & Impact

The visualization accurately renders the expected local stretching, rotation and distortion effects of the nonlinear transform, verified against hand-calculated reference points.

Future Improvements

  • Generalize to arbitrary complex functions via user input.
  • Add animated interpolation between transform states.
  • Connect to a concrete signal-processing use case.