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Automatul Celular - 1

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    De la automatul

    celular la Agenti inteligenti

    Florin Munteanu

    Nuanele raiunii umane pot contribui la raiuneaglobal a umanitii pentru constituirea unui modelontologic care s explice mai corect lumea material is ndrume tiina spre noi explorri i cunoatereriguroas.

    BlagaCafeneaua Complexitatii

    8 10 2012

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    FotoDavid Hall

    Proces cognitiv

    Descoperirevs. inovare

    Natural vs. Artificial

    Flux (Streaming) de informatii

    (reglare; declansare; diferentiere; feedback;feedbefore;)

    Flux de materie si energie

    observare

    Creatieartefacte

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    Ortofizica

    energie materie

    informatie

    ConstiintaUniversala

    E=mc2

    C1C2

    Cj

    cn

    MihaiDraganescu

    DavidChalmer

    HumbertoMaturana

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    Stiinta Computationala

    Domeniu de studiu dedicat intelegerii Naturiiprin abstractizarea principiilor fundamentale

    ce guverneaza fenomenul studiat si recreereaacestor dinamicin alte medii - de exemplu celnumeric, specific calculatorului - facndu-le

    astfel accesibile unor noi metode experimen-tale de manipulare si testare.

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    Un artefact ce provoaca

    omenirea: CALCULATORUL

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    T(i,j)

    http://www.youtube.com/watch?v=5ApSJe4FaLI&feature=related

    http://www.youtube.com/watch?v=5ApSJe4FaLI&feature=relatedhttp://www.youtube.com/watch?v=5ApSJe4FaLI&feature=relatedhttp://www.youtube.com/watch?v=5ApSJe4FaLI&feature=relatedhttp://www.youtube.com/watch?v=5ApSJe4FaLI&feature=related
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    Metoda relaxarii si automatulcelular ( mai putin decat o introducere doar pentrusurprinderea ideii )

    Derivata unei functiifin punctulxse poate aproxima ca raportul

    diferentelor finite:

    ( ) ( ) ( / 2) ( / 2)sau

    df f f x x f x f x x f x x

    dx x x x

    Sa folosim cea de a doua exprimare pentru a evalua derivata a doua

    2( / 2) ( / 2)

    22( ) ( ) 2 ( )x x x x

    df df

    dx dxd f d df f x x f x x f xdx dx dx x x

    Daca facem asta si pe directia y, si construim o retea patrata(x=y= ),

    obtinem aproximatia operatorului lui Laplace

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    continuare

    2

    2

    ( , ) ( , ) ( , ) ( , ) 4 ( , )( , )

    f x y f x y f x y f x y f x yf x y

    operatorul lui Laplace

    Ecuatia lui Laplace este echivalenta cu:2 0f

    1( , ) ( , ) ( , ) ( , ) ( , )

    4f x y f x y f x y f x y f x y

    11

    ( , ) ( 1, ) ( 1, ) ( , 1) ( , 1)4t tf i j f i j f i j f i j f i j

    la fiecare iteratie valoarea fiecarei celule esteinlocuita cu media aritmeticaa valorilor vecinilor(pastrand in acelasi timp valorile cerute lafrontiera)

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    1

    1( , ) ( 1, ) ( 1, ) ( , 1) ( , 1)

    4t tf i j f i j f i j f i j f i j

    23

    20 18

    29

    T(i,j)=1/4*(23+18+20+29)= 22.5

    t

    t+1Se copiaza starea t+1 (viitor) inmatricea t (prezent) si se reia operatia

    Proces recursiv

    Procesul se repeta pentru toate punctele(i,j) determinandu-se astfel starea la

    momentul t+1

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    Discretizare in spatiu

    Retea (patrata, triunghiulara,hexagonala, oarecare)

    Fiecare nod al retelei este un punct

    de masura (o entitate caracterizatade anumiti parametrii, o celula acarei stare se modifica in timpdependent de starea vecinilor)

    Problema frontierei (celule cuproprietati speciale)

    Iterare S(i,j)|t+1 =F(S(i-1,j),S(i+1,j),S(i,j-1),S(I,j+1), S(I,j))|t

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    Calitativ & Cantitativ

    y=F(x)x y

    X1= 1.25; F=x^2+0.5 x-1 ; y1= 1.1875X2=2.12; y2= 4.5544

    TRUNCHIERE la intreg =>Int(y1)= 1

    Int(y2)=4

    Definirea unui criteriu de taiere

    PAR/ IMPAR; Divizibil cu

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    Retea rectangulara de nxm celule

    S(k+1)=F(S(k))

    q11 q12 q13

    q21 q22 q23

    q31 q32 q33

    Q=

    Q={0,1, 0;1,-4,1;0,1,0}

    Q={1,4, 1;4,-20,4;1,4,1}

    T= Ax+B, unde A=Tdivx (partea intreaga); B=Tmod x (restul)

    Daca x=2 (mod 2) => regula de paritate deci S(I,j)|t+1=(1-B(ij))*(S(ij+1))|t

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    Q =| 2 1 2 ; 1 0 1 ; 2 1 2|

    0 0 0

    0 0

    0 0 1

    2 1 2

    1 0 1

    2 1 2

    0 0 0

    0 1 0

    0 0 1

    T=0+0+2*1=2 (PAR)

    Regula aleasa daca T este paratunci se activeaza celula tinta ;daca T este impar se inactiveazacelula tinta

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    AC- generator de numere

    W=S(I,j); W(n)

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    MODELARE vs.SIMULARE

    AUTO-O

    RGANIZARE

    EMERG

    ENTA

    Viata Artificiala

    http://www.wolfram.com/cdf-player/

    http://www.wolfram.com/cdf-player/http://www.wolfram.com/cdf-player/http://www.wolfram.com/cdf-player/http://www.wolfram.com/cdf-player/http://www.wolfram.com/cdf-player/http://www.wolfram.com/cdf-player/
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    SimulareDLA

    http://www.youtube.com/watch?v=uBy3Uouy76Q&feature=player_de

    tailpage#t=85s

    http://www.youtube.com/watch?v=uBy3Uouy76Q&feature=player_detailpagehttp://www.youtube.com/watch?v=uBy3Uouy76Q&feature=player_detailpagehttp://www.youtube.com/watch?v=uBy3Uouy76Q&feature=player_detailpagehttp://www.youtube.com/watch?v=uBy3Uouy76Q&feature=player_detailpage
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    Agenti inteligenti

    http://arieldolan.com/ofiles/Efloys.html

    http://arieldolan.com/ofiles/Efloys.htmlhttp://arieldolan.com/ofiles/Efloys.html
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    EXEMPLU

    http://localhost/var/www/apps/conversion/current/tmp/scratch_1/Efloys/Efloys.htmlhttp://localhost/var/www/apps/conversion/current/tmp/scratch_1/Efloys/Efloys.html
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    http://www.aridolan.com/http://www.calresco.org/http://alife.org/

    http://groups.engin.umd.umich.edu/CIS/course.des/cis479/projects/agent/Intelligent_agent.html

    http://www.aridolan.com/http://www.calresco.org/http://alife.org/http://groups.engin.umd.umich.edu/CIS/course.des/cis479/projects/agent/Intelligent_agent.htmlhttp://groups.engin.umd.umich.edu/CIS/course.des/cis479/projects/agent/Intelligent_agent.htmlhttp://groups.engin.umd.umich.edu/CIS/course.des/cis479/projects/agent/Intelligent_agent.htmlhttp://groups.engin.umd.umich.edu/CIS/course.des/cis479/projects/agent/Intelligent_agent.htmlhttp://alife.org/http://www.calresco.org/http://www.aridolan.com/
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    Multumesc pentru atentie


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