course material – g. tempesti gt512/bic.html course material will generally be available the day...
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Course material – G. Tempestihttp://www-users.york.ac.uk/~gt512/BIC.html
Course material will generally be available the day before the lecture
Includes PowerPoint slides and reading material
Ontogenetic systems
Drawing inspiration from growth and healing processes of living organisms…
…and applying them to electronic computing systems
Phylogeny (P)[Evolvability]
Epigenesis (E)[Adaptability]
Ontogeny (O)[Scalability]
PO hw
POE hw
OE hw
PE hw
Introduction
At the heart of the growth of a multi-cellular organism is the process of cellular division…
… aka (in computing) self-replication
Introduction In the 50s, John von Neumann wanted to build a
machine capable of self-replication
Mark II Aiken Relay Calculator (Harvard, 1947)
Introduction In the 50s, John von Neumann wanted to build a
machine capable of self-replication… but HOW?
Introduction In the 50s, John von Neumann wanted to build a
machine capable of self-replicationAt the same time, Stanislaw Ulam was working
on the computer-based realization of recursive patterns: geometric objects defined recursively.
Ulam suggested to Von Neumann to build an “abstract world”, controlled by well-defined rules, to analyze the logical principles of self-replication: this world is the world of cellular automata.
Cellular Automata (CA) Conceived by S.M. Ulam and J. von Neumann
Framework for the study of complex systems
Organized as a two-dimensional array of cells
Each cell can be in a finite number of states
Updated synchronously in discrete time steps
The state at the next time step depends of the current
states of the neighbourhood
The transitions are specified in a rule table
Environment states
0 =
1 =
2 =
3 =
4 =
etc…
Cellular Automata (CA)
Cellular Automata (CA)
Environment states neighbourhood
Wolfram (1-D)
Von Neumann
Moore (Life)
Cellular Automata (CA)
Environment states neighbourhood transition rules
== ==
== ==
Cellular Automata (CA)
Environment states neighbourhood transition rules
Configuration Initial state of the array
Wolfram’s Elementary CA
The simplest class of 1-D CA: two states (0 or 1), and rules that depend only on nearest neighbour values. Since there are 8 possible states for the three cells in a neighbourhood, there are a total of 256 elementary CA, each of which can be indexed with an 8-bit binary number.
Rule 30
Wolfram’s Elementary CA
Rule 30
Invented by John M. Conway (University of Cambridge)
Popularised by Martin Gardner (Scientific American, october 1970, february 1971)
Two-dimensional CATwo states per cell: dead and aliveEight neighbours (Moore)
2D CA: Game of Life
2D CA: Game of Life
• Birth of a cell
• Death of a cell
• Survival of a cell
• More than three neighbors• Less than three neighbors
• Two or three neighbors
• Three neighbors
2D CA: Game of Life
Gliders:
Glider gun:
Game of Life: the glider
Game of Life
Von Neumann’s CA
Environment
states = 29 neighborhood = von Neumann transition rules = 295 ~ 20M
Configuration
Initial state of the array ~ 200k cells for the constructor, > 1M for the memory tape
Von Neumann’s Constructor
Von Neumann’s Universal Constructor (Uconst) can build any finite machine (Ucomp), given its description D(Ucomp).
Uconst
D(Ucomp)M
Ucomp
M
Uconst
D(Uconst)
Von Neumann’s Constructor
Von Neumann’s Universal Constructor (Uconst) can build a copy of itself (Uconst’), given its own description D(Uconst).
Uconst'
D(Uconst)M'
Von Neumann’s Constructor
Von Neumann’s Universal Constructor (Uconst) can build a copy of itself (Uconst’) and of any finite machine (Ucomp’), given the description of both D(Uconst+Ucomp).
MUconstUcomp
D(Uconst+Ucomp)
M'
D(Uconst+Ucomp)
Ucomp' Uconst'
The universal constructor is a unicellular organism.
MOTHER CELL
DAUGHTER CELL
GENOME
Von Neumann’s Constructor Ordinary transmission states
Standard signal transmission paths (wires)
Non-excited:
Excited:
Input
InputInput
Output
Von Neumann’s Constructor Ordinary transmission states
Property 1: Transmission of excitations with a unit delay
Von Neumann’s Constructor Ordinary transmission states
Property 2: OR logic gate
Von Neumann’s Constructor Confluent states
Signal synchronization Non-directional (depends on neighbor’s direction)
Von Neumann’s Constructor Confluent states
Property 1: Introduction of double unit delay
Von Neumann’s Constructor Confluent states
Property 2: AND gate
Von Neumann’s Constructor Confluent states
Property 4: Fan-out
Von Neumann’s Constructor The XOR gate
Von Neumann’s Constructor The SR flip-flop
Von Neumann’s Constructor
Sensitive states Construction
Ordinary or special excitation
No excitation
Demonstration
Demonstration
Self-replicating CA After von Neumann, nothing much happened for
almost 30 years! Why? Probably because the hardware wasn’t
ready. In 1984, Chris Langton designed Langton’s Loop
Langton’s Loop Environment: 8 (?) states, 5 neighbours (von
Neumann), rules designed by hand Initial configuration: 94 active cells (vs. 200k+ in
von Neumann’s Universal Constructor) Replication occurs after 151 iterations
Langton’s Loop Aim: studying self-replication as “Artificial Life” Problem: does nothing but self-replicate
Langton’s Loop After Langton, the loops were optimized In one case (Perrier et al.) a Turing machine was
added to the loop (but at a high cost)
Towards functional self-replication Environment: 7+ states, 9 neighbours (Moore),
rules designed by hand Simple initial configuration, easily simulated
Towards functional self-replication Can be extended by adding “applications” (the
complexity depends on the task)