Art of Golden Ratio.ipynb

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    "from decimal import *\n",
    "import math\n",
    "from functools import reduce\n",
    "\n",
    "precision = 1000\n",
    "getcontext().prec = precision\n",
    "\n",
    "def get_constant(name):\n",
    "    if(name == 'phi'):\n",
    "        return str((Decimal(1) + Decimal(5) ** Decimal(0.5) )/ Decimal(2))\n",
    "    elif(name == 'pi'):\n",
    "        return str(sum(Decimal(1)/Decimal(16)**k * (Decimal(4)/(8*k+1) - Decimal(2)/(8*k+4) - Decimal(1)/(8*k+5) - Decimal(1)/(8*k+6)) for k in range(precision)))\n",
    "    elif(name == 'euler'):\n",
    "        return str(1 + sum(Decimal(1)/Decimal(math.factorial(x)) for x in range(1, 1000)))\n",
    "    elif(name == 'fibonacci'):\n",
    "        fib = lambda n: reduce(lambda x,n:[x[1],x[0]+x[1]], range(n),[0,1])[0]\n",
    "        return str(fib(precision))\n",
    "    else:\n",
    "        return str(sum(Decimal(1)/Decimal(10)**Decimal(x) for x in range(precision)))\n",
    "    \n",
    "# Select here which constant to use\n",
    "# Golden ratio = 'phi'\n",
    "constant = get_constant('phi')\n",
    "\n",
    "# Put all digits into list as discrete elements.  \n",
    "digits = []\n",
    "for x in range(2, len(constant)): \n",
    "    digits.append(int(constant[x:x+1]))"
   ]
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    "# Create starting vector\n",
    "x, y = [0], [0]\n",
    "\n",
    "for i in range(len(digits)-1):\n",
    "\n",
    "    # Digit to radians to vector\n",
    "    x_vector = math.sin(digits[i] / 10 * 2 * math.pi)\n",
    "    y_vector = math.cos(digits[i] / 10 * 2 * math.pi)\n",
    "\n",
    "    # Shift the current vector by the new one and add\n",
    "    x.append(x[i] + x_vector)\n",
    "    y.append(y[i] + y_vector)\n"
   ]
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   "source": [
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "colors = [\"#efb608\",\"#eda01c\",\"#e83923\",\"#dc265b\",\"#b62071\",\n",
    "          \"#88308a\",\"#5357ac\",\"#128195\",\"#18aa68\",\"#7fb853\"]\n",
    "\n",
    "i=0\n",
    "\n",
    "plt.figure(figsize=[5,5], dpi=300)\n",
    "\n",
    "for x1, x2, y1, y2 in zip(x, x[1:], y, y[1:]):\n",
    "    color_num = digits[i]\n",
    "    i = i + 1\n",
    "    plt.plot([x1, x2], [y1, y2], color=colors[color_num], linewidth=1,)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
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   ],
   "source": [
    "#%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm\n",
    "\n",
    "i=0\n",
    "\n",
    "plt.figure(figsize=[5,5], dpi=300)\n",
    "\n",
    "for x1, x2, y1, y2 in zip(x, x[1:], y, y[1:]):\n",
    "    plt.plot([x1, x2], [y1, y2], color=cm.viridis(i/precision), linewidth=1,)\n",
    "    i += 1\n",
    "    \n",
    "#plt.savefig('phi100000.svg');"
   ]
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