Faxina Simulation.ipynb

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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simulação de acúmulo de sujeira nos cantos do comodo\n",
    "## Durante aquela faxina de final de semana, daquela que é feita mais por não poder sair de casa durante a quarentena do que propriamente por asseio, é difícil não se irritar (ou se questionar) sobre o excesso de sujeira que fica acumulada nos cantos dos cômodos. No banheiro, nem se fala.\n",
    "\n",
    "## Isso talvez te leve ao questionamento (ou talvez simplesmente de tire o resto de paciência, faça você desistir da faxina e vá fazer outra coisa menos produtiva com o seu tempo, como escrever esse artigo, por exemplo) do porquê isso acontece. Será que existem Forças Ocultas dos Cantos que passam os dias usando seus poderes maléficos para dificultar ao máximo a sua tentativa de levar uma vida mais limpa e saudável?\n",
    "\n",
    "## Esse questionamento pode parecer exagerado, mas durante muito tempo essa questão tirou o meu sono (literalmente, principalmente durante as provas de fenômeno de transporte 3 na faculdade). Bom, não exatamente essa questão, mas muitas relacionadas á difusão e passeios aleatórios.\n",
    "\n",
    "## Difusão é um fenômeno que pra mim pareceu bizarro por muito tempo: como que diábos a batata dentro do arroz absorve o excesso de sal dentro da panela sem que haja uma força dentro da batata sugando esse sal?\n",
    "\n",
    "## Essa questão, no meu ponto de vista é extremamente profunda e filosófica, e mostra muito dos nossos viéses cognitivos como humanos e seres de narrativa.\n",
    "\n",
    "## Em narrativas em geral, ações são originiadas por agentes com intenções. Nos famosos contos de Arthur Connan Doyle, em que nosso héroi Sherlock Holmes consegue desvendar até aquilo que parece ser sobrenatural e inexplicável, a ação e intenção de agentes da narrativa sempre deixam traços, perceptíveis apenas para nosso héroi, que de forma determinística conclui com maestria o mistério, apresentando ao leitor a narrativa completa que descreve meticulosamente a ação dos agentes envolvidos no crime e suas intenções.\n",
    "\n",
    "## Como bem pontuou Yuval Harari diversas vezes em suas obras, a natureza não funciona como uma narrativa (ainda que muitas vezes não consigamos escapar das narrativas para fazer sentido do mundo). O problema da sujeira nas quinas, da batata no arroz e dos dessalinzadores de água do Kwait (poderia citar muitos outros) foram por muito tempo  instâncias desse \"viés da narrativa\" na minha vida.\n",
    "\n",
    "## Bem, vamos então desvendar esse mistério! A diferença é que ap invés de usarmos o método de redução analítica do nosso herói Sherlock, vamos usar um um pouco diferente, muito defendido por um grande expoente da Matemática e Computação do século XXI, conhecido também como o grande salvador dos estudantes de cálculo desesperados: Wolfram (O alpha). Wolfram propõe em seu livro \"a new kind o science\", a simulação como forma de tentar descrever fenômenos complexos. Fenômenos complexos é uma definição para fenômenos em que há uma grande interação entre agentes/forças, com efeitos aleatórios e determinísticos misturados -algo muito mais parecido com nossa vida real-. Uma forma muito comum de simulação é uma chamada Simulação Baseada em Agentes (Agent Based Modeling em ingles).\n",
    "\n",
    "\n",
    "## A Ideia então é, ao invés de buscar uma lei universal que rege a atração da poeira pelos cantos dos cômodos, vamos definir o comportamento total do sistema definindo o comportamento individual de suas partes e colocá-las para interagir com o ambiente em que se encontram e com seus pares.\n",
    "\n",
    "## Uma premissa filosófica bastante importante para nossa simulação será também a Navalha de oakan, extremamente importante na filosofia da ciência, que diz que: se dois modelos explicam igualmente bem a realidade, devemos escolher aquele que possui menos premissas\n",
    "\n",
    "## vamos então escolher um modelo com o mínimo de premissas possíveis\n",
    "\n",
    "## o elemento principal da nossa modelagem é o agente Particula. Esse agente tem dois atributos principais: sua posição em X e em Y\n",
    "\n",
    "## A nossa Particula performa uma unica ação (chamada de passo) que é se mover. A cada passo, a partícula pode se mover uma casa em X (esquerda/direita) e uma casa em Y(cima/baixo). O movimento da partícula é restrito de duas maneiras: caso ela encontra uma barreira (parede, por exemplo), ela não poderá ultrapassá-la. Além disso, vamos considerar que a força responsável pelo movimento da partícula é uma espécie de vento, que empurra a partícula. caso a partícula esteja bloqueada por alguma barreira, não há como a força agir pela face em que a partícula encontrou a barreira.\n",
    "\n",
    "## para facilitar nossos cálculos, usaremos um espaço discreto e tentaremos mitigar os efeitos disso criando um espaço de resolução alta (muitos pontos)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Chega de conversa e vamos à ação!\n",
    "Primeiro vamos definir os nossos agentes!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1268,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from tqdm.notebook import tqdm\n",
    "\n",
    "\n",
    "class Particula:\n",
    "\n",
    "    def __init__(self, x, y, espaco):\n",
    "        if espaco[x, y]:\n",
    "            self.x = x\n",
    "            self.y = y\n",
    "            self.gl = None\n",
    "\n",
    "        else:\n",
    "            raise ValueError('{} não é uma posição válida'.format((x, y)))\n",
    "\n",
    "    def passo(self, espaco):\n",
    "\n",
    "        if self.gl == 0:\n",
    "            return\n",
    "\n",
    "        movimentos_validos = [(0, 0), (0, 1), (0, -1), (1, 0),\n",
    "                              (1, 1), (1, -1), (-1, 0), (-1, 1), (-1, -1)]\n",
    "        vizinhanca = espaco[self.x-1:self.x+2, self.y-1:self.y+2]\n",
    "        if vizinhanca.mean() != 1:\n",
    "            x_rel, y_rel = (~vizinhanca).nonzero()\n",
    "            x_rel -= 1\n",
    "            y_rel -= 1\n",
    "            x_rel = np.concatenate([x_rel, -x_rel])\n",
    "            y_rel = np.concatenate([y_rel, -y_rel])\n",
    "\n",
    "            movimentos_invalidos = set(zip(x_rel, y_rel))\n",
    "            movimentos_validos = set(movimentos_validos) - movimentos_invalidos\n",
    "            self.gl = (len(movimentos_validos)-1)/(9-1)\n",
    "            if self.gl > 0:\n",
    "                movimento = choice(list(movimentos_validos))\n",
    "                self.x += movimento[0]\n",
    "                self.y += movimento[1]\n",
    "\n",
    "            return\n",
    "\n",
    "        movimento = choice(movimentos_validos)\n",
    "        self.x += movimento[0]\n",
    "        self.y += movimento[1]\n",
    "        self.gl = 1\n",
    "        return\n",
    "\n",
    "\n",
    "class Espaco:\n",
    "\n",
    "    def __init__(self, espaco_total, espaco_valido, densidade_de_particulas, observar=10, posicao_inicial=None):\n",
    "        assert espaco_total.shape == espaco_valido.shape\n",
    "        self.espaco_total = espaco_total\n",
    "        self.espaco_valido = espaco_valido\n",
    "\n",
    "        if not posicao_inicial:\n",
    "            posicoes = (np.random.random(espaco_valido.shape) <=\n",
    "                        densidade_de_particulas) & espaco_valido\n",
    "            posicoes = list(zip(*posicoes.nonzero()))\n",
    "        else:\n",
    "            assert posicao_inicial.__class__ == list\n",
    "            n = int(espaco.sum()*densidade_de_particulas)\n",
    "            posicoes = [choice(posicao_inicial) for i in range(n)]\n",
    "\n",
    "        particulas = [ParticulaComRestricao(pos[0], pos[1], self.espaco_valido)\n",
    "                      for pos in posicoes]\n",
    "        pasticulas_observadas = [choice(particulas) for i in range(observar)]\n",
    "        self.observador = {i: {j: [] for j in i.__dict__}\n",
    "                           for i in pasticulas_observadas}\n",
    "        self.particulas = particulas\n",
    "\n",
    "    def mostrar_espaco_total(self, **mplargs):\n",
    "        plt.imshow(self.espaco_total, cmap='gray', origin='lower')\n",
    "        posicoes_x = [p.x for p in self.particulas]\n",
    "        posicoes_y = [p.y for p in self.particulas]\n",
    "        plt.scatter(posicoes_y, posicoes_x, **mplargs)\n",
    "        pass\n",
    "\n",
    "    def mostrar_espaco_valido(self):\n",
    "        pass\n",
    "\n",
    "    def passo(self):\n",
    "        for particula in self.particulas:\n",
    "            particula.passo(self.espaco_valido)\n",
    "            if particula in self.observador:\n",
    "                for atributo in particula.__dict__:\n",
    "                    self.observador[particula][atributo].append(\n",
    "                        getattr(particula, atributo))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Nossa partícula é um agente extremamente simples. O méotodo __init__ inicializa nossa partícula e como sabemos, ela precisa ocupar um lugar no espaço, o parâmetro 'posicao' é a posição (x,y) da partícula no espaço. No método mover, movimentamos a partícula \n",
    "\n",
    "## Vamos definir o nosso espaço (tentarei fazer uma réplica do meu quarto) no paint e importá-lo usando a bibliotéca OpenCV do Python\n",
    "\n",
    "## é importante definirmos também qual o espaço permitido para a particula transitar, dado o espaço total."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1249,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(374, 749)"
      ]
     },
     "execution_count": 1249,
     "metadata": {},
     "output_type": "execute_result"
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#importar imagem\n",
    "quarto = cv2.imread('quarto_completo.png',0)\n",
    "#mostrar imagem\n",
    "plt.imshow(quarto, cmap='gray', origin = 'lower')\n",
    "#definir espaço permitido (área em branco)\n",
    "espaco = quarto == 255\n",
    "#printar dimensoes totais do quarto\n",
    "espaco.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## agora vamos criar nossa partícula e movimentá-la no espaço"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1250,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = Particula(150,100, espaco)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1258,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#posição inicial da partícula\n",
    "plt.imshow(quarto.T, cmap='gray')\n",
    "plt.scatter(p.x,p.y)\n",
    "#partícula se movimentando por 1000 intervalos de tempo\n",
    "x = [] \n",
    "y = []\n",
    "for i in range(1000):\n",
    "    p.passo(espaco)\n",
    "    x.append(p.x)\n",
    "    y.append(p.y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1259,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "MovieWriter ffmpeg unavailable; trying to use <class 'matplotlib.animation.PillowWriter'> instead.\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#histórico de posições no tempo\n",
    "fig, ax = plt.subplots()\n",
    "camera = Camera(fig)\n",
    "for x_,y_ in zip(x,y):\n",
    "    plt.imshow(quarto.T, cmap='gray')\n",
    "    plt.scatter(x_,y_, alpha = 1, s = 1, color = 'orange')\n",
    "    camera.snap()\n",
    "anim = camera.animate(blit=False, interval = 40)\n",
    "anim.save('uma_particula.gif')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Tudo certo para uma partícula! vamos agora simular diversas partículas no espaço"
   ]
  },
  {
   "attachments": {
    "uma_particula.gif": {
     "image/gif": 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    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![uma_particula.gif](attachment:uma_particula.gif)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1286,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "esp = Espaco(quarto, espaco, 0.01, 10, [(200,300),(350, 50),(150,500),(350,500),(300,550),(250,500),(300,50)])\n",
    "esp.mostrar_espaco_total(s = 0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## o numero de particulas é tal que a densidade de particulas (numero de particulas/ área disponível) é igual 1%. Iremos observar o histórico de 10 partículas selecionadas aleatoriamente e as partículas serão amontoadas igualmente em cada um desses pontos azuis no quarto, banheiro e corredor."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vamos agora rodar nossa simulação por 10.000 espaços de tempo e tirar uma 'foto' do quarto a cada 50 periodos de tempo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1287,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "21879ddc2dbc484a82c07830f8f47792",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=100000.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "camera = Camera(fig)\n",
    "fotos = []\n",
    "T = 100000\n",
    "C = 50\n",
    "c = 0\n",
    "for i in tqdm(range(T)):\n",
    "    esp.passo()\n",
    "    c += 1\n",
    "    if c == C:\n",
    "        posicoes_x = [p.x for p in esp.particulas]\n",
    "        posicoes_y = [p.y for p in esp.particulas]\n",
    "        fotos.append([posicoes_x,posicoes_y])       \n",
    "        c = 0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vamos ver agora o início e o fim da nossa simulação"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1293,
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1d5388db470>"
      ]
     },
     "execution_count": 1293,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(fotos[0][1],fotos[0][0],s = 10, alpha = 0.2)\n",
    "plt.imshow(quarto, cmap = 'gray')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1294,
   "metadata": {
    "cell_style": "split"
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.12742654279024096"
      ]
     },
     "execution_count": 1294,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "esp.mostrar_espaco_total(s = 10, alpha = 0.2)\n",
    "np.mean([i.gl for i in esp.particulas])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vamos agora observar a trajetória no tempo de uma das partículas observadas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1300,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1d3144f7f98>"
      ]
     },
     "execution_count": 1300,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#esp.mostrar_espaco_total(s = 0.4, alpha = 0.4)\n",
    "plt.imshow(quarto, cmap = 'gray')\n",
    "n = 4\n",
    "plt.scatter(esp.observador[list(esp.observador)[n]]['y'], esp.observador[list(esp.observador)[n]]['x'], s = 1, alpha = 0.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## E a evolução dos seus graus de liberdade"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1296,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1d538905d68>]"
      ]
     },
     "execution_count": 1296,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(range(len(esp.observador[list(esp.observador)[n]]['gl'])),esp.observador[list(esp.observador)[n]]['gl'], alpha = 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vamos agora gerar uma visualização dinâmica do nosso sistemainteiro"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1297,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "b211f3699eb249359ce33999027df60e",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=2000.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "MovieWriter ffmpeg unavailable; trying to use <class 'matplotlib.animation.PillowWriter'> instead.\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from celluloid import Camera\n",
    "plt.clf()\n",
    "fig,ax = plt.subplots()\n",
    "camera = Camera(fig)\n",
    "n = 0\n",
    "for i in tqdm(range(len(fotos))):\n",
    "    try:\n",
    "        plt.scatter(fotos[i][1],fotos[i][0],s = 5, alpha = 0.2, color = 'r')\n",
    "        plt.imshow(quarto, cmap = 'gray')        \n",
    "        camera.snap()        \n",
    "        n+=1\n",
    "    except: break\n",
    "\n",
    "anim = camera.animate(blit=False, interval = 40)\n",
    "anim.save('sim_visual.gif')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  },
  "latex_envs": {
   "LaTeX_envs_menu_present": true,
   "autoclose": false,
   "autocomplete": true,
   "bibliofile": "biblio.bib",
   "cite_by": "apalike",
   "current_citInitial": 1,
   "eqLabelWithNumbers": true,
   "eqNumInitial": 1,
   "hotkeys": {
    "equation": "Ctrl-E",
    "itemize": "Ctrl-I"
   },
   "labels_anchors": false,
   "latex_user_defs": false,
   "report_style_numbering": false,
   "user_envs_cfg": false
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}