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Mathematical Artwork in Python E-Book

Learn how to write Python code to create mathematically-based works of art. Without relying on any canned drawing libraries that do everything for you, the book will help the reader fully understand the math and code behind the images, using only the Numpy, Matplotlib, and Pillow libraries. A free sample can be downloaded here. The book assumes a basic knowledge of Python and some high-school level math.


1. Introduction

2. Math and Python Background

3. Computer Graphics

4. Parametric Methods

5. Randomness

6. Orbits and Escape Fractals

7. Orbit Trap Fractals

8. Orbit Density Fractals

9. The Buddhabrot

10. Color Theory

11. Composition

12. Polishing the Image

Appendix: Code methods

Appendix: About the book

The Code Listings + Wallpaper upgrade adds:

  • All the code examples in the book in ready-to-run Jupyter notebook format. No copy/paste required!
  • High-resolution images of "Leibniz 12" fractal in common desktop wallpaper resolutions (1280x720, 1366x768, 1440x900, 1536x864, 1600x900, 1920x1080, 3840x2160).

Leibniz 12 Fractal

The Interactive Code upgrade goes beyond the book by adding additional code to jump start your math-artist career:

  • Jupyter notebook with interactive Mandelbrot and Julia Set explorer. Click-and-drag to pan and zoom, all from a Jupyter notebook.
  • Interactive notebook for exploring Lissajous curves, harmonograph equation drawings, and spirograph equation drawings.
  • Interactive notebook for creating and exploring strange attractor plots.
  • Code for generating FFT-based sketches (in the style of Wolfram), and their parametric equations, by point-and-click.
  • Jupyter notebook for interactively creating color palettes
  • A list of 400 points in the complex plane, listed to 17 digits of precision, that iterate the Mandelbrot equation at least 1 million and up to 5 million times before escaping. Save your CPU when making high-resolution Buddhabrot fractals.

Screenshot of Interactive Strange Attractor running in Jupyter Notebook


Mathematical Artwork in Python E-Book

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