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comlex-function-visualization

A Python tool for creating beautiful visualizations and animations of complex function transformations. This program provides insights into how complex functions transform the complex plane through domain coloring and animated transitions.

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Overview

Languages: Python

Documentation

Complex Function Visualizer

A Python tool for creating beautiful visualizations and animations of complex function transformations. This program provides insights into how complex functions transform the complex plane through domain coloring and animated transitions.

Features

  • Domain coloring visualizations of complex functions
  • Phase and magnitude visualizations in separate plots
  • Animated transformations showing how functions map the complex plane
  • Custom HSV-based colormap for intuitive phase visualization
  • Support for a wide range of complex functions
  • Generates both static images (PNG) and animations (GIF)

Installation

  1. Clone this repository: 

    git clone [repository-url]
cd complex-function-visualizer

  2. Install the required dependencies: 

    pip install numpy matplotlib

Usage

Run the main script: 

python complex_visualizer.py

The program will generate: - Static visualizations for all example functions (saved as PNG files) - Animations for selected transformations (saved as GIF files) - Real-time display of all visualizations

Included Functions

The visualizer comes with several pre-defined complex functions: - f(z) = z² (Basic quadratic function) - f(z) = z³ - 1 (Cubic function with roots of unity) - f(z) = exp(z) (Complex exponential) - f(z) = sin(z) (Complex sine) - f(z) = z/(1-z) (Rational function) - f(z) = sqrt(z) (Complex square root) - f(z) = z·exp(z) (Product function) - f(z) = ln(1+z) (Complex logarithm)

Customization

You can easily add new functions or modify existing ones:

def create_example_functions():
    return [
        (lambda z: your_function(z), "f(z) = your_function_description"),
        # Add more functions here
    ]

Parameters to Adjust

  • size: Resolution of the visualization (default: 500)
  • x_range and y_range: Range of the complex plane to visualize
  • frames: Number of frames in animations (default: 50)

Output Files

The

[View full README on GitHub]