Iterated Functions
Fractals
L-Systems
Mandelbrot
Julia
Algorithmic Patterns
Symmetry
Introduction
One of the most basic kinds of numbers we will need are, of course, Complex Numbers. But what are they?
Complex Planes: What am \(i\)?
Dude, what’s the square root of -1?? 🙀 🙀 🙀!! And, what can you do repeatedly to arrive at \([-1, 0]\)?
- Complex Numbers are very useful in handling “2D data” in a compact fashion
- Complex Numbers help us to intuitively visualize, and implement, ideas such as rotation, scaling, and shadows, and projections.
- The duality between rotating vectors and complex numbers is a very important concept.
- Working with Shadows. https://www.wikiwand.com/en/Map_projection
- Working with Fourier Series and Epicyles http://www.jezzamon.com/fourier/index.html and https://alex.miller.im/posts/fourier-series-spinning-circles-visualization/
- https://twitter.com/i/status/962449509782495232 https://codegolf.stackexchange.com/questions/36374/redraw-an-image-with-just-one-closed-curve
Citation
BibTeX citation:
@online{2024,
author = {},
title = {\textless Iconify-Icon Icon=“tabler:math-Xy” Width=“1.2em”
Height=“1.2em”\textgreater\textless/Iconify-Icon\textgreater{}
{Complex} {Numbers}},
date = {2024-05-02},
url = {https://mathforcoders.netlify.app/content/courses/MathModelsDesign/Modules/25-Geometry/20-ComplexNumbers/},
langid = {en}
}
For attribution, please cite this work as:
“<Iconify-Icon Icon=‘tabler:math-Xy’
Width=‘1.2em’
Height=‘1.2em’></Iconify-Icon> Complex
Numbers.” 2024. May 2, 2024. https://mathforcoders.netlify.app/content/courses/MathModelsDesign/Modules/25-Geometry/20-ComplexNumbers/.