biologically-inspired computing lecture 7 Informatics luis rocha 2015 biologically Inspired computing INDIANA UNIVERSITY

Transcription

1 lecture 7 -inspired

2 Sections I485/H400 course outlook Assignments: 35% Students will complete 4/5 assignments based on algorithms presented in class Lab meets in I1 (West) 109 on Lab Wednesdays Lab 0 : January 14 th (completed) Introduction to Python (No Assignment) Lab 1 : January 8 th Measuring Information (Assignment 1) Due February 11 th Lab : February 11 th L-Systems (Assignment ) Due February 5 th Lab 3: March 11 th Cellular Automata and Boolean Networks (Assignment 3)

3 Readings until now Class Book Nunes de Castro, Leandro [006]. Fundamentals of Natural Computing: Basic Concepts, Algorithms, and Applications. Chapman & Hall. Chapter 8 - Artificial Life Chapter 7, sections 7.1, 7. and 7.4 Fractals and L-Systems Appendix B.3.1 Production Grammars Lecture notes Chapter 1: What is Life? Chapter : The logical Mechanisms of Life Chapter 3: Formalizing and Modeling the World posted Papers and other materials Life and Information Kanehisa, M. [000]. Post-genome Informatics. Oxford University Press. Chapter 1. Logical mechanisms of life (H400, Optional for I485) Langton, C. [1989]. Artificial Life In Artificial Life. C. Langton (Ed.). Addison-Wesley. pp Optional Flake s [1998], The Computational Beauty of Life. MIT Press. Chapter 1 Introduction Chapters 5, 6 (7-9) Self-similarity, fractals, L-Systems

4 Drawing words Turtle graphics δ= 90 state of turtle defined as (x, y, α), coordinates (position) and angle (heading). Moves according to step size d and angle increment δ From: P. Prusinkiewicz and A. Lindenmayer [1991]. The Algorithmic Beauty of Plants.

5 Alphabet handling by Turtle An L-system is an ordered triplet G = <V, w, P> V = alphabet of the symbols in the system V = {F, X} w = nonempty word the axiom: X P = finite set of production rules (productions) X F[+X][-X]FX F FF L-systems Alphabet V {X,F,[,],+,-} Drawing Procedure (Turtle) {X,F,[,],+,-} Angle: 14

6 Alphabet handling by Turtle Example L-System V = {F, X} axiom: X Productions X F[+X][-X]FX F FF Alphabet V {X,F,[,],+,-} L-systems Turtle {X,F,[,],+,-} n=1 F[+X][-X]FX F[+][-]F FF n= FF[+F[+X][-X]FX][-F[+X][-X]FX]FF[+X][-X]FX FF[+F[+][-]F][-F[+][-]F]FF[+][-]F FF[+FF][-FF]FFF

7 Alphabet handling by Turtle n= FF[+F[+X][-X]FX][-F[+X][-X]FX]FF[+X][-X]FX FF[+F[+][-]F][-F[+][-]F]FF[+][-]F FF[+FF][-FF]FFF L-systems n=3 FFFF[+FF[+F[+X][-X]FX][-F[+X][-X]FX]FFF[+X][-X]FX][-FF[+ F[+X][-X]FX][-F[+X][-X]FX]FFF[+X][-X]FX]FFFF[+F[+X][-X]FX][- F[+X][-X]FX]FFF[+X][-X]FX FFFF[+FF[+F[+][-]F][- F[+][-]F]FF F[+][-]F][-FF[+ F[+][-]F][- F[+][- ]F]FF F[+][-]F]FFFF[+ F[+][-]F][- F[+][-]F]FFF[+][-]F FFFF[+FF[+FF][-FF]FFFF][-FF[+FF][-FF]FFFF]FFFF[+FF][-FF]FFFF Angle: 14

8 Alphabet handling by Turtle (adding color) Example L-System V = {F, X} axiom: X Productions X F[>8+X][>8-X]FX F FF L-systems Alphabet V {X,F,[,],+,-,>n} Turtle {X,F,[,],+,-,>n}

9 example Turtle graphics From: P. Prusinkiewicz and A. Lindenmayer [1991]. The Algorithmic Beauty of Plants.

10 robots automatic design of basic shapes Evolutionary design of robots Difficult to reach high complexities necessary for practical engineering Karl Sims and Jordan Pollack, Hod Lipson, Gregory Hornby, and Pablo Funes claim that for automatic design to scale in complexity it must employ re-used modules generative representation to encode individuals in the population. Indirect representation: an algorithm for creating a design. using Lindenmayer systems (L-systems) evolved locomotiong robots (called genobots).

11 Hertzian modeling paradigm Modeling the World The most direct and in a sense the most important problem which our conscious knowledge of nature should enable us to solve is the anticipation of future events, so that we may arrange our present affairs in accordance with such anticipation. (Hertz, 1894) Model Symbols (Images) Initial Conditions Formal Rules (syntax) Logical Consequence of Model Predicted Result???? Observed Result (Pragmatics) Encoding (Semantics) Measure Measure World 1 Physical Laws World

12 Models or realistic imitations? L-systems Common features (design principle) between artificial and real plants Development of (macro-level) morphology from local (micro-level) logic Parallel application of simple rules Genetic vs. algorithmic Recursion But are the algorithms the same? Real organisms need to economize information for coding complex phenotypes The genome cannot encode every ripple of the brain or lungs Organisms need to encode compact procedures for producing the same pattern (with randomness) again and again But recursion alone does not explain form and morphogenesis One of the design principles involved There are others Selection, genetic variation, self-organization, epigenetics fern gametophyte Microsorium linguaeforme (left) and a simulated model using map L systems (right).

13 exploring similarities across nature Natural design principles self-similar structures Trees, plants, clouds, mountains morphogenesis Mechanism Iteration, recursion, feedback Dynamical Systems and Unpredictability From limited knowledge or inherent in nature? Mechanism Chaos, measurement Collective behavior, emergence, and self-organization Complex behavior from collectives of many simple units or agents cellular automata, ant colonies, development, morphogenesis, brains, immune systems, economic markets Mechanism Parallelism, multiplicity, multi-solutions, redundancy Adaptation Evolution, learning, social evolution Mechanism Reproduction, transmission, variation, selection, Turing s tape Network causality (complexity) Behavior derived from many inseparable sources Environment, embodiment, epigenetics, culture Mechanism Modularity, connectivity, stigmergy

14 bodies in motion dynamical systems Mathematical models of systems containing the rules describing the way some quantity undergoes a change in time What changes in time a variable Position, quantity, concentration How does something change in time Deterministic rules that define change Set of differential equations defining rates of change

15 gravitational pendulum example What changes in time a variable Angle Rules that define change Set of differential equations defining rates of change dynamical systems F mg sin a g sin ma d s a dt d l dt d l dt g sin l d dt g sin 0

16 chemical reaction example dynamical systems What changes in time a variable concentrations Rules that define change Set of differential equations defining rates of change dx dt dx dt dx dt 1 f1( x1, x) x1 K1x x 1 f x1, x3) 3 f ) 3 x1 ( x K x ( K x x x 3

17 phase or state-space Map of variables in time Time is parameter Trajectory (orbit) in state space x dynamical systems x 1 X ( t) x1 ( t), x( t), x3( t) Continuous (reversible) systems Only one trajectory passes through each point of a state-space State-determined system points on different trajectories will always be on different trajectories Albeit arbitrarily close Determinism, strict causality Laplace Not true in discrete systems x 3 x x 3 x 1

18 vector fields in phase-space dynamical systems

19 readings Next lectures Class Book Nunes de Castro, Leandro [006]. Fundamentals of Natural Computing: Basic Concepts, Algorithms, and Applications. Chapman & Hall. Chapter, all sections Chapter 7, sections 7.3 Cellular Automata Chapter 8, sections 8.1, 8., Lecture notes Chapter 1: What is Life? Chapter : The logical Mechanisms of Life Chapter 3: Formalizing and Modeling the World posted Papers and other materials Optional Flake s [1998], The Computational Beauty of Life. MIT Press. Chapters 10, 11, 14 Dynamics, Attractors and chaos