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 Sections I485/H400 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 28 th Measuring Information (Assignment 1) Due February 11 th Lab 2 : February 11 th biologically L-Systems (Assignment 2) Inspired computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics Readings until now luis rocha 2015 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 biologically Inspired computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics Modeling the World luis rocha 2015 Hertzian modeling paradigm “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) Predicted Result Logical Model el Symbols I nitial Consequence ???? Conditions (I mages) of Model Formal Rules Observed Result (syntax) (Pragmatics) Encoding (Semantics) Measure Measure Physical Laws biologically World 2 World 1 Inspired computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics Natural design principles luis rocha 2015 exploring similarities across nature 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 biologically Mechanism Inspired Modularity, connectivity, stigmergy computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics Coastlines luis rocha 2015 Lewis Richardson's observations (1961) 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. biologically Inspired computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics luis rocha 2015 biologically Inspired computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics regular volumes luis rocha 2015 Integer dimensions biologically Inspired computing rocha@indiana.edu INDIANA Scientific American , July 2008 UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics dimension of fractal curves luis rocha 2015 the Koch curve example: fractional dimensions n =0 Koch curve slightly more than line but less than a plane Packing efficiency! n =1 a=1 unit (meter) n =2 N=4 n n →∞ a=1/3 n Hausdorff Dimension Measuring Number of units scale D log N log 4 1 log N = = = = ⇒ = D 1 . 26186 ... N D 1 log 3 1 a log biologically log a Inspired a computing Unit measure rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics re-writing design principle luis rocha 2015 mathematical monsters 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 →∞ log N = = 0 . 6309 D 1 log biologically Scientific American , July 2008 a Inspired computing Hausdorff Dimension rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics re-writing design principle luis rocha 2015 mathematical monsters 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 log N biologically = = 1 . 585 D Inspired 1 log computing Scientific American , July 2008 a rocha@indiana.edu INDIANA Hausdorff Dimension UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics re-writing design principle luis rocha 2015 mathematical monsters 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 log biologically N = = D 2 . 7268 Inspired 1 computing log Scientific American , July 2008 a rocha@indiana.edu INDIANA Hausdorff Dimension UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics dimension of fractal curves luis rocha 2015 Box-counting dimension Number of boxes ε log N ( ) = D lim ε → 1 0 log ε Length of box biologically side Inspired computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics Peano and Hilbert Curves luis rocha 2015 Filling planes and volumes Hilbert Peano biologically Inspired computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics fractal features luis rocha 2015 Self-similarity on multiple scales Due to recursion Fractal dimension Enclosed in a given space, but with infinite number of points or measurement biologically Inspired computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics fractal-like designs in Nature luis rocha 2015 reducing volume How do these packed volumes and biologically Inspired recursive morphologies grow? computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
What about our plant? Info rm atics luis rocha 2015 An Accurate Model Requires Varying angles Varying stem lengths randomness The Fibonacci Model is similar Initial State: b b -> a a -> ab sneezewort b b b a a a b a b b a a b a b Psilophyta/Psilotum a biologically Inspired b computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
Info rm atics L-Systems luis rocha 2015 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 biologically Parallel recursion Inspired Access to computers computing rocha@indiana.edu INDIANA UNIVERSITY http://informatics.indiana.edu/rocha/i-bic
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