Notes - Pages 115-222

Cellular Automata in number systems
cellular automata depend on local information, number systems at the digit level can show similar behavior because the digits have variance and depend on the operation on them. The author uses binary representation, obersving basic patterns in common operations 3*n, and complex patterns from f(n) = g(f(n-1)), i.e. mappings that have a recursive definition
124
Iterated maps
mapping [0,1]->[0,1] through a set of rules or operations
149
continous automata
instead of binary, 0,1 convert to grayscale [0,1]. There is a similarity between continous automata and differential equations. Both depend on local information. Most studied diff eqs have a correspondingly simple continous automata, the more complex ones tend to be less so, and or ignored possibly due to difficulty of analysing them.
155-167
multi-dimension
3D automata can be sliced into 2D automata which can be sliced into 1D automata.
171-177
automata as graphs
an alternatrive way to represent automata, used to show time variance between states of the automata
193-200
constaints
given a set of constraints, form a 1D 'string', always simple patterns. Add more dimensions, then complexity comes in but only if a exhaustive set of patterns cannot be found within the produced output. (217)
210-220

  • Chapter 4 - How to relate automata to numbers by breaking numbers down into parts and relating the parts (digit sequences). Also going from discrete to continous is simple and can produce all the same structures seen in the previous chapters.

  • Chapter 5 - Extending these ideas from the linear 1 dimension model to 2 dimensions and 3 dimensions. Each N dimension automata is composed of (N-1) dimension slices that themselves are automata in the (N-1) dimension. The first few instances of the author making the case that traditioanl mathematics had not dealt with complexity because constraint based systems to show complexity need complex constraints and are rare in those systems.