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
What sort of literature do you fancy in the evening? Simon’s downloaded the book The Algorithmic Beauty of Plants tonight.
Here Simon explained to me how L-systems and Cantor Set worked:
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”.
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
And “what you also might need by an L-system is a String Buffer”: