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)