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Info rm atics biologically-inspired computing luis rocha 2015 lecture 6 biologically Inspired computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic Info rm atics course outlook luis rocha 2015

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rocha@indiana.edu http://informatics.indiana.edu/rocha/i-bic

biologically Inspired computing

INDIANA UNIVERSITY

Informatics luis rocha 2015

biologically-inspired computing lecture 6

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biologically Inspired computing

rocha@indiana.edu http://informatics.indiana.edu/rocha/i-bic

INDIANA UNIVERSITY

Informatics luis rocha 2015

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 14th (completed)

 Introduction to Python (No Assignment)

 Lab 1 : January 28th

 Measuring Information (Assignment 1)  Due February 11th

 Lab 2 : February 11th

 L-Systems (Assignment 2)

Sections I485/H400

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biologically Inspired computing

rocha@indiana.edu http://informatics.indiana.edu/rocha/i-bic

INDIANA UNIVERSITY

Informatics luis rocha 2015

Readings until now

Class Book

Nunes de Castro, Leandro [2006]. Fundamentals of Natural Computing: Basic Concepts, Algorithms, and Applications. Chapman & Hall.

 Chapter 8 - Artificial Life  Chapter 7, sections 7.1, 7.2 and 7.4 – Fractals and L-Systems  Appendix B.3.1 – Production Grammars

Lecture notes

 Chapter 1: “What is Life?”  Chapter 2: “The logical Mechanisms of Life”  Chapter 3: Formalizing and Modeling the World

 posted online @ http://informatics.indiana.edu/rocha/i-bic

Papers and other materials

Life and Information

 Kanehisa, M. [2000]. 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. 1-47.

Optional

 Flake’s [1998], The Computational Beauty of Life. MIT Press.

 Chapter 1 – Introduction  Chapters 5, 6 (7-9) – Self-similarity, fractals, L-Systems

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biologically Inspired computing

rocha@indiana.edu http://informatics.indiana.edu/rocha/i-bic

INDIANA UNIVERSITY

Informatics luis rocha 2015

Modeling the World World1

Measure

Symbols (I mages) I nitial Conditions

Measure

Logical Consequence

  • f Model

Model el

Formal Rules (syntax)

World2

Physical Laws Observed Result Predicted Result

????

Encoding

(Semantics)

(Pragmatics)

“The most direct and in a sense the most important problem which our conscious knowledge of nature should enable us to solve is the ant nt icipat ion n of fut ut ur ure eve vent nt s, so that we may arrange our present affairs in accordance with such anticipation”. (Hertz, 1894)

Hertzian modeling paradigm

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biologically Inspired computing

rocha@indiana.edu http://informatics.indiana.edu/rocha/i-bic

INDIANA UNIVERSITY

Informatics luis rocha 2015

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

exploring similarities across nature

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biologically Inspired computing

rocha@indiana.edu http://informatics.indiana.edu/rocha/i-bic

INDIANA UNIVERSITY

Informatics luis rocha 2015

Coastlines

Measured maps with different scales

Coasts of Australia, South Africa, and Britain

Land frontiers of Germany and Portugal

Measured lengths L(d) at different scales d.

 As the scale is reduced, the length increases

rapidly.

Well-fit by a straight line with slopes (s) on log/log plots

 s = -0.25 for the west coast of Britain, one of

the roughest in the atlas,

 s = -0.15 for the land frontier of Germany,  s = -0.14 for the land frontier of Portugal,  s = -0.02 for the South African coast, one of

the smoothest in the atlas.

 circles and other smooth curves have line of

slope 0.

Lewis Richardson's observations (1961)

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biologically Inspired computing

rocha@indiana.edu http://informatics.indiana.edu/rocha/i-bic

INDIANA UNIVERSITY

Informatics luis rocha 2015

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biologically Inspired computing

INDIANA UNIVERSITY

Informatics luis rocha 2015 Integer dimensions

regular volumes

Scientific American, July 2008

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biologically Inspired computing

rocha@indiana.edu http://informatics.indiana.edu/rocha/i-bic

INDIANA UNIVERSITY

Informatics luis rocha 2015

dimension of fractal curves

 Koch curve

 slightly more than line but less

than a plane

 Packing efficiency!

N=4n

the Koch curve example: fractional dimensions

a=1/3n Measuring scale

... 26186 . 1 3 log 4 log 1 log log = =       = a N D

      = ⇒       = a N D a N

D

1 log log 1

Unit measure Number of units Hausdorff Dimension

n =0 n =1 n =2 n →∞

a=1 unit (meter)

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biologically Inspired computing

rocha@indiana.edu http://informatics.indiana.edu/rocha/i-bic

INDIANA UNIVERSITY

Informatics luis rocha 2015

re-writing design principle

Complex objects are defined by systematically and recursively replacing parts of a simple start object with another object according to a simple rule

 Cantor Set

n =0 n =1 n =2 n →∞

mathematical monsters

Scientific American, July 2008

6309 . 1 log log =       = a N D

Hausdorff Dimension

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biologically Inspired computing

rocha@indiana.edu http://informatics.indiana.edu/rocha/i-bic

INDIANA UNIVERSITY

Informatics luis rocha 2015

re-writing design principle

Complex objects are defined by systematically and recursively replacing parts of a simple start object with another object according to a simple rule

 Sierpinski Gasket

mathematical monsters

585 . 1 1 log log =       = a N D

Hausdorff Dimension

Scientific American, July 2008

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biologically Inspired computing

rocha@indiana.edu http://informatics.indiana.edu/rocha/i-bic

INDIANA UNIVERSITY

Informatics luis rocha 2015

re-writing design principle

Complex objects are defined by systematically and recursively replacing parts of a simple start object with another object according to a simple rule

 Menger sponge

mathematical monsters

7268 . 2 1 log log =       = a N D

Hausdorff Dimension

Scientific American, July 2008

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biologically Inspired computing

INDIANA UNIVERSITY

Informatics luis rocha 2015 Box-counting dimension

dimension of fractal curves

      =

→

ε ε

ε

1 log ) ( log lim N D

Length of box side

Number of boxes

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biologically Inspired computing

INDIANA UNIVERSITY

Informatics luis rocha 2015 Filling planes and volumes

Peano and Hilbert Curves

Peano Hilbert

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rocha@indiana.edu http://informatics.indiana.edu/rocha/i-bic

INDIANA UNIVERSITY

Informatics luis rocha 2015

fractal features  Self-similarity on multiple scales

 Due to recursion

 Fractal dimension

 Enclosed in a given space, but with infinite

number of points or measurement

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biologically Inspired computing

INDIANA UNIVERSITY

Informatics luis rocha 2015

fractal-like designs in Nature

reducing volume

How do these packed volumes and recursive morphologies grow?

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biologically Inspired computing

rocha@indiana.edu http://informatics.indiana.edu/rocha/i-bic

INDIANA UNIVERSITY

Informatics luis rocha 2015

What about our plant?

An Accurate Model

Requires

 Varying angles  Varying stem

lengths

 randomness

The Fibonacci Model is similar

 Initial State: b  b -> a  a -> ab

sneezewort

Psilophyta/Psilotum

b a b b b b b b b b a a a a a a a

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biologically Inspired computing

rocha@indiana.edu http://informatics.indiana.edu/rocha/i-bic

INDIANA UNIVERSITY

Informatics luis rocha 2015

L-Systems

 Mathematical formalism

proposed by the biologist Aristid Lindenmayer in 1968 as a foundation for an axiomatic theory of biological development.

 applications in computer graphics

 Generation of fractals and realistic

modeling of plants

 Grammar for rewriting Symbols

 Production Grammar  Defines complex objects by

successively replacing parts of a simple object using a set of recursive, rewriting rules or productions.

 Beyond one-dimensional

production (Chomsky) grammars

 Parallel recursion  Access to computers

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biologically Inspired computing

rocha@indiana.edu http://informatics.indiana.edu/rocha/i-bic

INDIANA UNIVERSITY

Informatics luis rocha 2015

L-systems  An L-system is an ordered triplet

 G = <V, w, P>

 V = alphabet of the symbols in the system

 V = {F, B}

 w = nonempty word

 the axiom: B

 P = finite set of production rules (productions)

 B → F[-B][+B]  F → FF

formal notation of the production system

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rocha@indiana.edu http://informatics.indiana.edu/rocha/i-bic

INDIANA UNIVERSITY

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branching L-Systems

Add branching symbols [ ]

 Main trunk shoots off one

side branch

 simple example

 Angle 45  Axiom: F  Seed Cell  Rule: F=F[+F]F

Deterministic, context-free L-systems

 Simplest class of L-

systems

 Simple re-writing  D0L

F F [+ F]

production rules for artificial plants

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biologically Inspired computing

rocha@indiana.edu http://informatics.indiana.edu/rocha/i-bic

INDIANA UNIVERSITY

Informatics luis rocha 2015

L-system with 2 cell types  Axiom

 B

 Cell Types

 B,F

 Rules

 B → F[-B][+B]  F → FF

Depth Resulting String

B

1

F[-B]+B

2

FF[-F[-B]+B]+ F[-B]+B

3

FFFF[-FF[- F[-B]+B]+ FF[-B]+B]+ F[- F[-B]+B]+ F[-B]+B

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rocha@indiana.edu http://informatics.indiana.edu/rocha/i-bic

INDIANA UNIVERSITY

Informatics luis rocha 2015

parametric L-systems

 Discrete nature of L-

systems makes it difficult to model continuous phenomena

 Numerical parameters are

associated with L-system symbols

 Parameters control the

effect of productions

 A ( t )  B ( t x 3)

 Growth can be modulated by

time

 Varying length of braches,

rotation degrees

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biologically Inspired computing

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Informatics luis rocha 2015 example

parametric L-system

  • perate on parametric

words, which are strings of modules consisting of symbols with associated parameters and their rules

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

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rocha@indiana.edu http://informatics.indiana.edu/rocha/i-bic

INDIANA UNIVERSITY

Informatics luis rocha 2015

stochastic L-systems

 Probabilistic production rules

 A  B C ( P = 0.3 )  A  F A ( P = 0.5 )  A  A B ( P = 0.2 ) http://coco.ccu.uniovi.es/malva/sketchbook/

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INDIANA UNIVERSITY

Informatics luis rocha 2015

Context-sensitive L-systems

 Production rules depend on neighbor symbols in

input string

 simulates interaction between different parts

 necessary to model information exchange between

neighboring components

 2L-Systems

 P: al < a > ar  X

 P1: A<F>A  A  P2: A<F>F  F

 1L-Systems

 P: al < a  X or P: a > ar  X

 Generalized to IL-Systems

 (k,l)-system

 left (right) context is a word of length k(l)

2L-Systems

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biologically Inspired computing

INDIANA UNIVERSITY

Informatics luis rocha 2015 example

parametric 2L-system

convenient tool for expressing developmental models with diffusion of substances. pattern of cells in Anabaena catenula and

  • ther blue-green

bacteria

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

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SLIDE 27

biologically Inspired computing

rocha@indiana.edu http://informatics.indiana.edu/rocha/i-bic

INDIANA UNIVERSITY

Informatics luis rocha 2015

Next lectures

Class Book

Nunes de Castro, Leandro [2006]. Fundamentals of Natural Computing: Basic Concepts, Algorithms, and Applications. Chapman & Hall.

 Chapter 7, sections 7.1, 7.2 and 7.4 – Fractals and L-Systems  Appendix B.3.1 – Production Grammars

 Lecture notes

 Chapter 1: What is Life?  Chapter 2: The logical Mechanisms of Life  Chapter 3: Formalizing and Modeling the World

 posted online @ http://informatics.indiana.edu/rocha/i-bic

Papers and other materials

 Logical mechanisms of life (H400, Optional for I485)

 Langton, C. [1989]. “Artificial Life” In Artificial Life. C. Langton

(Ed.). Addison-Wesley. pp. 1-47.

 Optional

 Flake’s [1998], The Computational Beauty of Life. MIT Press.

 Chapter 1 – Introduction  Chapters 5, 6 (7-9) – Self-similarity, fractals, L-Systems

 Prusinkiewicz and Lindenmeyer [1996] The algorithmic beauty

  • f plants.

 Chapter 1

readings