tupper's formula

tuppers.ipynb

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   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
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   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "from mpmath import mp\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%pylab inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[Tupper's formula](https://en.wikipedia.org/wiki/Tupper%27s_self-referential_formula)\n",
    "\n",
    "$$ \\frac{1}{2} < \\left \\lfloor{ \\text{mod}\\left ( \\left \\lfloor{\\frac{y}{17}} \\right \\rfloor 2^{-17 \\lfloor{x}\\rfloor - \\text{mod} \\left ( \\lfloor{y}\\rfloor, 17 \\right )} \\right ) } \\right \\rfloor $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "metadata": {
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   "outputs": [],
   "source": [
    "mp.prec = 2000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def tupper_field(k):\n",
    "    field = np.ndarray((17,106), np.bool)\n",
    "    for xix, x in enumerate(mp.arange(0,106)):\n",
    "        for yix, y in enumerate(mp.arange(k,k+17)):\n",
    "            t1 = mp.floor(y) % 17\n",
    "            t2 = -17*mp.floor(x)\n",
    "            t3 = 2**(t2 - t1)\n",
    "            t4 = mp.floor(y/17)\n",
    "            t5 = (t4 * t3) % 2\n",
    "            field[16-yix, xix] = 0.5 < mp.floor(t5)\n",
    "    return field"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "k1 = mp.mpf('820959624942020445814005879832445494830930')\n",
    "k2 = mp.mpf('4858450636189713423582095962494202044581400587983244549483093085061934704708809928450644769865524364849997247024915119110411605739177407856919754326571855442057210445735883681829823754139634338225199452191651284348332905131193199953502413758765239264874613394906870130562295813219481113685339535565290850023875092856892694555974281546386510730049106723058933586052544096664351265349363643957125565695936815184334857605266940161251266951421550539554519153785457525756590740540157929001765967965480064427829131488548259914721248506352686630476300')"
   ]
  },
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   "execution_count": 182,
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   ],
   "source": [
    "for k in [k1,k2]:\n",
    "    f = tupper_field(k)\n",
    "    ax = plt.imshow(f, cmap='Greys', interpolation='nearest')\n",
    "    ax.axes.axis('off')\n",
    "    plt.show()"
   ]
  }
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