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Course material – G. Tempesti. http://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. Phylogeny (P) [Evolvability]. PO hw. PE hw. POE hw. Ontogeny (O) [Scalability]. OE hw.

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## Course material – G. Tempesti

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**Course material – G. Tempesti**http://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**Phylogeny (P)**[Evolvability] PO hw PE hw POE hw Ontogeny (O) [Scalability] OE hw Epigenesis (E) [Adaptability] Ontogenetic systems Drawing inspiration from growth and healing processes of living organisms… …and applying them to electronic computing systems**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-replication At 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 CA Two states per cell: dead and alive Eight neighbours (Moore) 2D CA: Game of Life**2D CA: Game of Life**• Birth of a cell • Three neighbors • Death of a cell • More than three neighbors • Less than three neighbors • Survival of a cell • Two or three neighbors**Gliders:**Glider gun: Game of Life: the glider**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).**Von Neumann’s Constructor**Von Neumann’s Universal Constructor (Uconst) can build a copy of itself (Uconst’), given its own description D(Uconst).**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). DAUGHTER CELL MOTHER CELL GENOME The universal constructor is a unicellular organism.**Von Neumann’s Constructor**Ordinary transmission states Standard signal transmission paths (wires) Non-excited: Excited: Input Input Input 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**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)

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