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"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"require 'gsl'\n",
"require 'nyaplot'\n",
"require 'nyaplot3d'\n",
"require 'nyaplot_utils'"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
""
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 1,
"text": [
"\"if(window['d3'] === undefined ||\\n window['Nyaplot'] === undefined){\\n var path = {\\\"d3\\\":\\\"http://d3js.org/d3.v3.min\\\"};\\n\\n\\n\\n var shim = {\\\"d3\\\":{\\\"exports\\\":\\\"d3\\\"}};\\n\\n require.config({paths: path, shim:shim});\\n\\n\\nrequire(['d3'], function(d3){window['d3']=d3;console.log('finished loading d3');\\n\\n\\tvar script = d3.select(\\\"head\\\")\\n\\t .append(\\\"script\\\")\\n\\t .attr(\\\"src\\\", \\\"http://cdn.rawgit.com/domitry/Nyaplotjs/master/release/nyaplot.js\\\")\\n\\t .attr(\\\"async\\\", true);\\n\\n\\tscript[0][0].onload = script[0][0].onreadystatechange = function(){\\n\\n\\n\\t var event = document.createEvent(\\\"HTMLEvents\\\");\\n\\t event.initEvent(\\\"load_nyaplot\\\",false,false);\\n\\t window.dispatchEvent(event);\\n\\t console.log('Finished loading Nyaplotjs');\\n\\n\\t};\\n\\n\\n});\\n}\\n\""
]
},
{
"html": [
""
],
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"text": [
"\"if(window['d3'] === undefined ||\\n window['Nyaplot'] === undefined){\\n var path = {\\\"d3\\\":\\\"http://d3js.org/d3.v3.min\\\",\\\"THREE\\\":\\\"http://cdnjs.cloudflare.com/ajax/libs/three.js/r66/three.min\\\",\\\"Elegans\\\":\\\"http://cdn.rawgit.com/domitry/elegans/nyaplot-extension/release/elegans\\\"};\\n\\n\\n\\n var shim = {\\\"d3\\\":{\\\"exports\\\":\\\"d3\\\"},\\\"THREE\\\":{\\\"exports\\\":\\\"THREE\\\"},\\\"Elegans\\\":{\\\"exports\\\":\\\"Elegans\\\"}};\\n\\n require.config({paths: path, shim:shim});\\n\\n\\nrequire(['d3'], function(d3){window['d3']=d3;console.log('finished loading d3');require(['THREE'], function(THREE){window['THREE']=THREE;console.log('finished loading THREE');require(['Elegans'], function(Elegans){window['Elegans']=Elegans;console.log('finished loading Elegans');\\n\\n\\tvar script = d3.select(\\\"head\\\")\\n\\t .append(\\\"script\\\")\\n\\t .attr(\\\"src\\\", \\\"http://cdn.rawgit.com/domitry/Nyaplotjs/master/release/nyaplot.js\\\")\\n\\t .attr(\\\"async\\\", true);\\n\\n\\tscript[0][0].onload = script[0][0].onreadystatechange = function(){\\n\\n\\n\\t var event = document.createEvent(\\\"HTMLEvents\\\");\\n\\t event.initEvent(\\\"load_nyaplot\\\",false,false);\\n\\t window.dispatchEvent(event);\\n\\t console.log('Finished loading Nyaplotjs');\\n\\n\\t};\\n\\n\\n});});});\\n}\\n\""
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{
"metadata": {},
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"text": [
"true"
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{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Modified Chua's attractor"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"http://en.wikipedia.org/wiki/Multiscroll_attractor#Modifed_Chua_chaotic_attractor"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"alpha = 10.82\n",
"beta = 14.286\n",
"a = 1.3\n",
"b = 0.1\n",
"d = 0.2\n",
"func = lambda {|x| return -b*Math.sin((Math::PI*x)/(2*a)+d)}\n",
"\n",
"ode_func = Proc.new { |t, y, dydt, mu|\n",
" dydt[0] = alpha*(y[1] - func.call(y[0]))\n",
" dydt[1] = y[0] - y[1] + y[2]\n",
" dydt[2] = -beta*y[1]\n",
"}\n",
"\n",
"solver = GSL::Odeiv::Solver.alloc(GSL::Odeiv::Step::RK8PD, [1e-11, 0.0], ode_func, 3)\n",
"\n",
"t = 0.0 # initial time\n",
"t1 = 250.0 # end time\n",
"h = 1e-11 # initial step\n",
"y = GSL::Vector.alloc([0, 0.49899, 0.2]) # initial value\n",
"mat = []\n",
"\n",
"while t < t1\n",
" t, h, status = solver.apply(t, t1, h, y)\n",
" break if status != GSL::SUCCESS\n",
" mat.push([t, y[0],y[1],y[2]])\n",
"end"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 2
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"mat = mat.transpose\n",
"df = Nyaplot::DataFrame.new({t: mat[0], x: mat[1], y: mat[2], z: mat[3]})\n",
"df"
],
"language": "python",
"metadata": {},
"outputs": [
{
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"| t | x | y | z |
|---|
| 1.0e-11 | 5.6140320159400467e-11 | 0.4989899999970101 | 0.1999999999287143 |
| 6.0e-11 | 3.368419209623403e-10 | 0.4989899999820606 | 0.19999999957228576 |
| 3.0999999999999996e-10 | 1.740349925125477e-09 | 0.49898999990731313 | 0.19999999779014296 |
| 1.5599999999999998e-09 | 8.757889949652093e-09 | 0.49898999953357565 | 0.19999998887942905 |
| 7.809999999999998e-09 | 4.384559016505851e-08 | 0.4989899976648881 | 0.19999994432585955 |
| 3.9059999999999994e-08 | 2.1928409356142367e-07 | 0.4989899883214497 | 0.19999972155801454 |
| 1.9530999999999997e-07 | 1.0964766685265609e-06 | 0.49898994160423993 | 0.19999860771885214 |
| 9.765599999999998e-07 | 5.482440992932909e-06 | 0.498989708017746 | 0.1999930385246043 |
| 4.882809999999999e-06 | 2.7412298854215525e-05 | 0.49898854007414783 | 0.19996519259247092 |
| 2.4414059999999998e-05 | 0.0001370624941086894 | 0.49898270007796175 | 0.19982596390948346 |
| 0.00012207030999999998 | 0.0006853361149292664 | 0.4989534931443302 | 0.19912984494054012 |
| 0.0006103515599999999 | 0.0034272698123728063 | 0.4988072849312846 | 0.19564986174628682 |
| 0.0030517578099999994 | 0.01715101233505604 | 0.49807193929518095 | 0.17826529924258544 |
| 0.014013795507761044 | 0.0790538904376299 | 0.4946849710419077 | 0.10052883063525046 |
| 0.04982410837893326 | 0.2841840439075322 | 0.48277542201961954 | -0.14954917089523478 |
| 0.09110818347184979 | 0.5248197579585029 | 0.4678452220897041 | -0.4299299960466015 |
| ... | ... | ... | ... |
| 250.0 | -5.400855387922898 | 0.009052459747508661 | 5.576075334785507 |
"
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]
}
],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"color = Nyaplot::Colors.GnBu"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"| rgb(247,252,240) | rgb(224,243,219) | rgb(204,235,197) | rgb(168,221,181) | rgb(123,204,196) | rgb(78,179,211) | rgb(43,140,190) | rgb(8,104,172) | rgb(8,64,129) |
|---|
| | | | | | | | | |
"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 4,
"text": [
"#"
]
}
],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fill = color.to_a[4]"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 5,
"text": [
"\"rgb(123,204,196)\""
]
}
],
"prompt_number": 5
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot = Nyaplot::Plot.new\n",
"line = plot.add_with_df(df, :line, :x, :y)\n",
"line.color(fill)\n",
"line.stroke_width(1)\n",
"plot"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"\n"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 6,
"text": [
"#[#:line, :options=>{:x=>:x, :y=>:y, :color=>\"rgb(123,204,196)\", :stroke_width=>1}, :data=>\"e34ea2fc-b31a-4498-8ccd-6ad9ecfa9a39\"}, @xrange=[-10.824798558907991, 5.542798924206478], @yrange=[-0.47441920746466154, 0.4989899999970101]>], :options=>{:zoom=>true, :width=>700, :xrange=>[-10.824798558907991, 5.542798924206478], :yrange=>[-0.47441920746466154, 0.4989899999970101]}}>"
]
}
],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot = Nyaplot::Plot3D.new\n",
"plot.add_with_df(df, :line, :x, :y, :z)\n",
"plot"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"\n"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 7,
"text": [
"#[#:line, :options=>{:x=>:x, :y=>:y, :z=>:z}, :data=>\"e34ea2fc-b31a-4498-8ccd-6ad9ecfa9a39\"}>], :options=>{}, :extension=>\"Elegans\"}>"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Tamari attractor"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"a=1.013; b=-0.021;c=0.019;d=0.96;e=0;f=0.01;g=1;u=0.05;i=0.05\n",
"ode_func = Proc.new { |t, y, dydt, mu|\n",
" dydt[0] = (y[0]-a*y[1])*Math.cos(y[2])-b*y[1]*Math.sin(y[2])\n",
" dydt[1] = (y[0]+c*y[1])*Math.sin(y[2])+d*y[1]*Math.cos(y[2])\n",
" dydt[2] = e + f*y[2] + g*Math.atan(((1-u)*y[1]) / (1-i)*y[0])\n",
"}\n",
"\n",
"solver = GSL::Odeiv::Solver.alloc(GSL::Odeiv::Step::RK8PD, [1e-10, 0.0], ode_func, 3)\n",
"\n",
"t = 0.0\n",
"t1 = 800.0\n",
"h = 1e-10\n",
"y = GSL::Vector.alloc([0.9,1,1])\n",
"mat = []\n",
"\n",
"while t < t1\n",
" t, h, status = solver.apply(t, t1, h, y)\n",
" break if status != GSL::SUCCESS\n",
" mat.push([y[0],y[1],y[2]])\n",
"end\n",
"\n",
"mat = mat.transpose\n",
"df = Nyaplot::DataFrame.new({x: mat[0], y: mat[1].map{|v| -v}, z:mat[2]})"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"| x | y | z |
|---|
| 0.8999999999956617 | -1.0000000001292002 | 1.0000000000742815 |
| 0.8999999999739701 | -1.0000000007752012 | 1.000000000445689 |
| 0.8999999998655119 | -1.0000000040052064 | 1.000000002302727 |
| 0.899999999323221 | -1.0000000201552321 | 1.0000000115879157 |
| 0.8999999966117648 | -1.0000001009053614 | 1.0000000580138615 |
| 0.8999999830544468 | -1.0000005046560325 | 1.0000002901436267 |
| 0.8999999152669365 | -1.0000025234100083 | 1.0000014507933692 |
| 0.8999995763063614 | -1.00001261719538 | 1.0000072540650027 |
| 0.8999978809279204 | -1.0000630865095295 | 1.0000362709961745 |
| 0.8999893896488653 | -1.0003154427574013 | 1.000181369975517 |
| 0.8999465738691381 | -1.0015774652831169 | 1.0009072227557285 |
| 0.8997235465350497 | -1.0078935295674298 | 1.0045454082648322 |
| 0.8983894240339892 | -1.0396124064085692 | 1.0229561732510872 |
| 0.8875157865156315 | -1.1941600240857642 | 1.116262513449279 |
| 0.865546231137117 | -1.4020117288496465 | 1.2537947751345435 |
| 0.8421368106796103 | -1.632630964895723 | 1.4343762499054211 |
| ... | ... | ... |
| -0.135753889231557 | 0.7047282984780947 | 4.567022194880662 |
"
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{
"cell_type": "code",
"collapsed": false,
"input": [
"color = Nyaplot::Colors.GnBu"
],
"language": "python",
"metadata": {},
"outputs": [
{
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"| rgb(247,252,240) | rgb(224,243,219) | rgb(204,235,197) | rgb(168,221,181) | rgb(123,204,196) | rgb(78,179,211) | rgb(43,140,190) | rgb(8,104,172) | rgb(8,64,129) |
|---|
| | | | | | | | | |
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"text": [
"#"
]
}
],
"prompt_number": 9
},
{
"cell_type": "code",
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"input": [
"plot = Nyaplot::Plot.new\n",
"line = plot.add_with_df(df, :line, :y, :x)\n",
"line.stroke_width(0.3)\n",
"line.color(color.to_a[5])\n",
"plot"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"\n"
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"output_type": "pyout",
"prompt_number": 10,
"text": [
"#[#:line, :options=>{:x=>:y, :y=>:x, :stroke_width=>0.3, :color=>\"rgb(78,179,211)\"}, :data=>\"a50d542f-bba7-4f2e-8595-8fbc9c71afdc\"}, @xrange=[-1.9753449401078695, 1.6519733822511717], @yrange=[-0.6239742227056861, 1.353995956514491]>], :options=>{:zoom=>true, :width=>700, :xrange=>[-1.9753449401078695, 1.6519733822511717], :yrange=>[-0.6239742227056861, 1.353995956514491]}}>"
]
}
],
"prompt_number": 10
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot.export_contents 'context.svg'"
],
"language": "python",
"metadata": {},
"outputs": []
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plot = Nyaplot::Plot3D.new\n",
"plot.add_with_df(df, :line, :x, :y, :z)\n",
"plot"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"\n",
"\n"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 14,
"text": [
"#[#:line, :options=>{:x=>:x, :y=>:y, :z=>:z}, :data=>\"a50d542f-bba7-4f2e-8595-8fbc9c71afdc\"}>], :options=>{}, :extension=>\"Elegans\"}>"
]
}
],
"prompt_number": 14
}
],
"metadata": {}
}
]
}