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:

Biology, Coding, Geometry Joys, Java, Murderous Maths


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


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