06

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Video recordings lecture 1
Video recordings lecture 2

Fractals

Introduction

• Linton, Oliver. Fractals. Wooden Books, 2019. https://woodenbooks.com/index.php?#!FRC.
• Mandelbrot, Benoît B., and Nial Neger. “Fractal Geometry,” Yale University, 2020. https://users.math.yale.edu/public_html/People/frame/Fractals/.

Plants

• Prusinkiewicz, Przemyslaw, and Aristid Lindenmayer. The Algorithmic Beauty of Plants. The Virtual Laboratory. New York, NY: Springer New York, 1990. https://doi.org/10.1007/978-1-4613-8476-2.
• Twitter thread of tree generators : https://twitter.com/GalaxyKate/status/1329901625281028097

Geography

• Jiang, Bin. “New Paradigm in Mapping: A Critique on Cartography and GIS,” January 17, 2019. https://doi.org/10.20944/preprints201901.0173.v1.
• Jiang, Bin. “Head/Tail Breaks for Visualization of City Structure and Dynamics.” Cities 43 (March 1, 2015): 69–77. https://doi.org/10.1016/j.cities.2014.11.013.

Complex Numbers

• Sanderson, Grant. Euler’s Formula with Introductory Group Theory, 2017. https://www.youtube.com/watch?v=mvmuCPvRoWQ.

Studio

All code files can be found here: https://github.com/jbenno/nyuad_decoding_nature/tree/master/Files/06

Recursion

• Factorial n!=n*(n-1)!
• Fibonacci sequence f(n)=f(n-1)*f(n-2)
• Fibonacci sequence iterative with a loop instead of recursion
• Fibonacci sequence as sequence of squares illustrating the Golden Section
• Cantor Set
• Barycentric division
• Circles

Self-similarity

• Sierpinsky Triangle
• Sierpinsky Tetrahedron
• Mis en abyme - Video feedback loop

Fractals

• Pythagoras tree
• Using the Pythagoras tree algorithm to create a fractal with endless abyss
• Tree with branches
• Barnsley Fern

Complex numbers

• The basic algebra including a class for complex numbers
• Domain Colouring
• Image transformation
• The Mandelbrot Set with domain colouring
• Mandelbrot Set
• Julia Set

Chaos and strange attractors

• Lorenz Attractor
• Henon Attractor
• Logistic function - attractor demo
• Logistic Bifurcation

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