Murderous Maths, Simon teaching, Simon's sketch book

Infinities Driving You Mad. Part 2: There’re Infinitely Many Infinities

This is the second part in a series of four videos that Simon is recording about Infinities Driving You Mad (on Set Theory) and is devoted to ordinal numbers. If you would like a little more explanation about what ω-one is, please see this short footnote video where Simon explains in more detail how he moves from the first infinite ordinal ω to ω-one:

Link to Part 1 about cardinal numbers: https://youtu.be/jyOnxdJHWOU

Biology, Coding, Geometry Joys, Java, Murderous Maths

L-Systems

What sort of literature do you fancy in the evening? Simon’s downloaded the book The Algorithmic Beauty of Plants tonight.

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Here Simon explained to me how L-systems and Cantor Set worked:

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An L-system or Lindenmayer system is a parallel rewriting system and a type of formal grammar. An L-system consists of an alphabet of symbols that can be used to make strings, a collection of production rules that expand each symbol into some larger string of symbols, an initial “axiom” string from which to begin construction, and a mechanism for translating the generated strings into geometric structures.

Simon says that an L-sestem is “also a context-free grammar that can have infinite generations”.

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The Cantor set is a set of points lying on a single line segment that has a number of remarkable and deep properties.

Simon followed the book and Daniel Shiffman’s tutorial on L-Systems to create beautiful trees and other recursive patterns in

http://turtleacademy.com/playground/en

and

http://www.kevs3d.co.uk/dev/lsystems/#

L_System Fractal Trees 15 Apr 2017 1

L_System Fractal Trees 15 Apr 2017 2 square brackets around last F

L_System Fractal Trees 15 Apr 2017 2

L_System Fractal Trees 15 Apr 2017 23

L_System Fractal Trees 15 Apr 2017 4

And “what you also might need by an L-system is a String Buffer”:

String Buffer (might need by L system) 15 Apr 2017 2