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@fperez
Created July 13, 2016 04:23
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The "Batman curve" in Julia
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Batman curve in Julia\n",
"\n",
"As [described in this short overview](https://sinews.siam.org/DetailsPage/tabid/900/ArtMID/2243/ArticleID/431/Default.aspx) of Julia for SIAM News, by Alan Edelman.\n",
"\n",
"We start by defining the bat functions: semicircle, ellipse, shoulders, bottom, cowl:"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"σ(x) = √(1-x.^2)\n",
"el(x) = 3σ(x/7)\n",
"s(x) = 4.2 - .5x -2.8σ(.5x - .5)\n",
"b(x) = σ(abs(2-x)-1)-x.^2/11 + .5x -3\n",
"c(x) = [1.7, 1.7, 2.6, .9];"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, plot symmetrically acros y-axis (NaNs lift the \"pen\"):"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x31e53bd68>)"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"using PyPlot\n",
"p(x,f) = plot([-x; 0; x], [f(x); NaN; f(x)])\n",
"p(3:.1:7, el); p(4:.1:7, t-> -el(t)) # ellipse\n",
"p(1:.1:3, s); p(0:.1:4, b) # shoulders and bottom\n",
"p([0,.5,.8,1], c); # cowl is piecewise linear;"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Julia 0.4.5",
"language": "julia",
"name": "julia-0.4"
},
"language_info": {
"file_extension": ".jl",
"mimetype": "application/julia",
"name": "julia",
"version": "0.4.5"
},
"widgets": {
"state": {},
"version": "1.1.2"
}
},
"nbformat": 4,
"nbformat_minor": 1
}
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