lambdaway :: randomwalk

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{center Rafraîchir la page pour voir la réalisation de 8 autres marches aléatoires.}

_h1 random walks

_p Following:
_ul [[https://fr.wikipedia.org/wiki/Marche_aléatoire|https://fr.wikipedia.org/wiki/Marche_aléatoire]]
_ul [[codespeedy|https://www.codespeedy.com/random-walk-program-in-python/]]
_ul [[https://fr.acervolima.com/random-walk-implementation-en-python/|https://fr.acervolima.com/random-walk-implementation-en-python/]]
_ul [[https://www.lptmc.jussieu.fr/user/sator/Chapitre2.pdf|https://www.lptmc.jussieu.fr/user/sator/Chapitre2.pdf]]
_ul [[https://www.techno-science.net/glossaire-definition/Marche-aleatoire|https://www.techno-science.net/glossaire-definition/Marche-aleatoire-page-3.html]]
_ul ...

_p Chaque courbe représente une marche aléatoire. Chaque pas du marcheur se fait selon une des 4 directions (vers l'est, l'ouest, le nord ou le sud). Le choix de la direction de chaque pas est issu du hasard, avec équiprobabilité pour chacune des éventualités. Voir la preuve à la page [[frequency3]].

{pre
;; {A.sort! < {A.new {S.map walk.direction {S.serie 0 100}}}}

'{def walk.direction           // -> [0 1 2 3] -> EAST, WEST, NORTH, SOUTH
 {lambda {} 
  {floor {* 4 {random}}}}}    // merci Christophe
-> {def walk.direction    ;; Math.floor(Math.random() * (max - min + 1)) + min
 {lambda {} {floor {* 4 {random}}}}}

'{def walk.u
 {lambda {:u :dir :step}
        {if {= :dir 0} then {+ :u :step}
   else {if {= :dir 1} then {- :u :step}
   else :u }} }}       // les deux autres cas, 2 & 3
-> {def walk.u
 {lambda {:u :dir :step}
  {if {= :dir 0}
   then {+ :u :step}
   else {if {= :dir 1} 
   then {- :u :step}
   else :u }} }}

'{def walk.v
 {lambda {:v :dir :step}
        {if {= :dir 2} then {+ :v :step}
   else {if {= :dir 3} then {- :v :step}
   else :v }} }}       // les deux autres cas 0 & 1
-> {def walk.v
 {lambda {:v :dir :step}
  {if {= :dir 2} 
   then {+ :v :step}
   else {if {= :dir 3} 
   then {- :v :step}
   else :v }} }}

'{def walk
 {def walk.rec
  {lambda {:x :y :step :n :i}
   {if {= :i :n}
    then {A.new :x :y}
    else {let { {:x :x} {:y :y} {:step :step} {:n :n} {:i :i}
                {:dir {walk.direction}}
              } {walk.rec {A.addlast! {walk.u {A.get {- :i 1} :x} :dir :step} :x}
                          {A.addlast! {walk.v {A.get {- :i 1} :y} :dir :step} :y}
                          :step
                          :n
                          {+ :i 1}}}}}}
 {lambda {:x :y :step :n}
  {walk.rec {A.new :x} {A.new :y} :step :n 1}}}  
-> {def walk
 {def walk.rec
  {lambda {:x :y :step :n :i}
   {if {= :i :n}
    then {A.new :x :y}
    else {let { {:x :x} {:y :y} {:step :step} {:n :n} {:i :i}
                {:dir {walk.direction}}

} {walk.rec {A.addlast! {walk.u {A.get {- :i 1} :x}
                                              :dir
                                              :step}
                                      :x}
                          {A.addlast! {walk.v {A.get {- :i 1} :y}
                                              :dir
                                              :step}
                                      :y}
                   :step
                   :n
                   {+ :i 1}}}}}}
 {lambda {:x :y :step :n}
  {walk.rec {A.new :x} {A.new :y} :step :n 1}}}

'{def XY 
 {lambda {:x :y :step :n}
  {S.map {{lambda {:xy :i} 
                {A.get :i {A.first :xy}} {A.get :i {A.last :xy}}   
          } {walk :x :y :step :n}}   
         {S.serie 1 :n}}}} 
-> {def XY 
 {lambda {:x :y :step :n}
  {S.map {{lambda {:xy :i} 
                {A.get :i {A.first :xy}} {A.get :i {A.last :xy}}   
          } {walk :x :y :step :n}}   
         {S.serie 1 :n}}}}

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}

_p {i 2022/10/18}

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}}
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