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    "# <font color=\"blue\">section4_1.ipynb</font>\n",
    "\n",
    "<font color=\"red\">PYTHON, Apprentissage Actif, JP. ROY, ELLIPSES 2020</font>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from turtle_init import *\n",
    "# from turtle import *\n",
    "# init(x=0,y=0,cap=0)\n",
    "# afficher(msg,x,y)\n",
    "# sleep(dt)            en secondes flottantes\n",
    "# deg_rad(a_degrés)    conversion degrés -> radians\n",
    "# rot(M,K,a_degrés)    K = centre de rotation\n",
    "# segment(M1,M2)       le tracé d'un segment\n",
    "# pi, sqrt, sin, cos, randint   pour les calculs fréquents"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def poly_cart(n,a,b,r):\n",
    "    '''Dessine un polygone régulier ayant n côtés inscrit\n",
    "    dans un cercle de rayon r et de centre (a,b).'''\n",
    "    up() ; goto(a+r,b) ; down()             # départ au pôle Est\n",
    "    alpha = 2 * pi / n                      # radians pour la trigo\n",
    "    for k in range(1,n+1):\n",
    "        goto(a + r * cos(k * alpha), b + r * sin(k * alpha))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def poly_pol(n,c):\n",
    "    '''Dessine un polygone régulier ayant n côtés,\n",
    "    côté ayant une longueur c, à partir de la position\n",
    "    courante de la tortue.'''\n",
    "    a = 360 / n\n",
    "    for i in range(n):\n",
    "        forward(c)\n",
    "        left(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "def von_koch(n,L):     # approximant de niveau n, base de longueur L\n",
    "    if n == 0 :\n",
    "        forward(L)                           # le générateur\n",
    "    else :\n",
    "        von_koch(n-1,L/3)                    # 4 appels récursifs !\n",
    "        left(60)\n",
    "        von_koch(n-1,L/3)\n",
    "        right(120)\n",
    "        von_koch(n-1,L/3)\n",
    "        left(60)\n",
    "        von_koch(n-1,L/3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "if __name__ == '__main__':\n",
    "    reset()           # effacement canvas graphique, init. tortue au centre\n",
    "    tracer(False)     # début tracé immédiat\n",
    "    afficher('Tracé en cartésien',0,220)\n",
    "    poly_cart(7,0,0,200)\n",
    "    poly_cart(4,100,50,50)\n",
    "    tracer(True)      # fin tracé immédiat\n",
    "    getcanvas().postscript(file='polygone7_4.ps')   # création d'un fichier disque\n",
    "\n",
    "    tracer(False)\n",
    "    poly_cart(40,-200,200,30)    # polygone régulier de 40 côtés : quasi-cercle\n",
    "    tracer(True)      # fin tracé immédiat\n",
    "    sleep(4)\n",
    "\n",
    "    # tracé lent, cette fois en polaire, à l'endroit où est la tortue\n",
    "    reset()\n",
    "    afficher('Tracé en polaire (mode lent)',0,-100)\n",
    "    poly_pol(7,100)\n",
    "    sleep(2)\n",
    "\n",
    "    # la fractale de von Koch, niveaux 0..7\n",
    "    reset()\n",
    "    tracer(False)\n",
    "    for i in range(8):\n",
    "        reset()\n",
    "        init(-285,0,0)                     # à gauche, cap Est\n",
    "        von_koch(i,285*2)\n",
    "        afficher('Von Koch, niveau {}'.format(i),0,-100)\n",
    "        sleep(2)\n",
    "    tracer(True)\n",
    "    getcanvas().postscript(file='von_koch.ps')  # fichier Postscript sur le disque\n",
    "\n",
    "    # Lancement de la boucle d'évènements (bloquante) dans la fenêtre tortue\n",
    "    mainloop()\n",
    "    print('Fini.')     # une fois la fenêtre fermée..."
   ]
  }
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