Figure_1c.ipynb

{
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  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots\n",
    "using Random\n",
    "using Distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "simpler_jump (generic function with 2 methods)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function simpler_jump(x, y, a = 1)\n",
    "    theta = rand(Uniform(0, 2 * π))\n",
    "    u = rand(Uniform(0, 1))\n",
    "\n",
    "    r = a/(3 * u)^(1/3)\n",
    "\n",
    "    xfl = r * sin(theta)\n",
    "    yfl = r * cos(theta)\n",
    "\n",
    "    (floor(Int, x + xfl + 1/2),\n",
    "    floor(Int, y + yfl + 1/2), r)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hist = [];\n",
    "for i in 1:100_000\n",
    "    (newx, newy, dist) = simpler_jump(0, 0)\n",
    "    push!(hist, dist)\n",
    "end\n",
    "\n",
    "histogram(hist, xlims=(0, 10), legend = false, title = \"Jump Function Histogram\", xguide = \"Distance of Jump\", yguide = \"Frequency\")"
   ]
  }
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