如何用数学软件画一个“圣诞树”?-Python Tutorial-php.cn

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如何用数学软件画一个“圣诞树”?

WBOYWBOYWBOYWBOYWBOYWBOYWBOYWBOYWBOYWBOYWBOYWBOYWB

Jun 06, 2016 pm 04:22 PM

可以是字符的，也可以是图形的

相关问题如何用C语言画一个“圣诞树”? - 编程

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我只是搬运http://codegolf.stackexchange.com上的答案，原作者是Silvia （@Silvia )，用的是Mathematica。

PD = .5;
s[t_, f_] := t^.6 - f
dt[cl_, ps_, sg_, hf_, dp_, f_, flag_] :=
    Module[{sv, basePt},
           {PointSize[ps],
            sv = s[t, f];
            Hue[cl (1 + Sin[.02 t])/2, 1, .3 + sg .3 Sin[hf sv]],
            basePt = {-sg s[t, f] Sin[sv], -sg s[t, f] Cos[sv], dp + sv};
            Point[basePt],
           If[flag,
              {Hue[cl (1 + Sin[.1 t])/2, 1, .6 + sg .4 Sin[hf sv]], PointSize[RandomReal[.01]],
               Point[basePt + 1/2 RotationTransform[20 sv, {-Cos[sv], Sin[sv], 0}][{Sin[sv], Cos[sv], 0}]]},
              {}]
          }]

frames = ParallelTable[
                       Graphics3D[Table[{
                                         dt[1, .01, -1, 1, 0, f, True], dt[.45, .01, 1, 1, 0, f, True],
                                         dt[1, .005, -1, 4, .2, f, False], dt[.45, .005, 1, 4, .2, f, False]},
                                        {t, 0, 200, PD}],
                                  ViewPoint -> Left, BoxRatios -> {1, 1, 1.3}, 
                                  ViewVertical -> {0, 0, -1},
                                  ViewCenter -> {{0.5, 0.5, 0.5}, {0.5, 0.55}}, Boxed -> False,
                                  PlotRange -> {{-20, 20}, {-20, 20}, {0, 20}}, Background -> Black],
                       {f, 0, 1, .01}];

Export["tree.gif", frames]

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Mathematica版本：
打开一个notebook，然后长按CTRL+/,效果如下：

像不像一棵圣诞树呢？这里有用SAS画的圣诞树，翻译成了Mathematica版的

Clear["`*"];
ifs[prob_,A_,init_,max_]:=FoldList[#2.{#[[1]],#[[2]],1}&,init,RandomChoice[prob->A,max]];

L={{{0.03,0},{0,0.1}},{{0.85,0},{0,0.85}},{{0.8,0},{0,0.8}},{{0.2,-0.08},{0.15,0.22}},{{-0.2,0.08},{0.15,0.22}},{{0.25,-0.1},{0.12,0.25}},{{-0.2,0.1},{0.12,0.2}}};
B=Map[List,{{0,0},{0,1.5},{0,1.5},{0,0.85},{0,0.85},{0,0.3},{0,0.4}},{2}];

{A,prob,init,max}={N@Join[L,B,3],{2,60,10,7,7,7,7}/100.,{0.,2.},10^5};
pts=ifs[prob,A,init,max];//AbsoluteTiming
Graphics[{{Darker@Green,PointSize@Tiny,Point@pts},{Hue@Random[],PointSize@Large,Point@#}&/@RandomChoice[pts,200]},AspectRatio->1.5]

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去年用R画了圣诞树送给教定量入门的教授，改了一下Wiekvoet: Merry Christmas的代码。
（今年直接手动涂色送happy spring的卡片了，不是程序媛搞不出酷炫的东西好桑心） Wolfram Mathematica 算数学软件吧？

还有这个：

算不算抖机灵 = = 鸡汁的我

MATLAB ，名副其实的数学软件。

参考 File Exchange
by Anselm Ivanovas
====================================
%

<span class="k">function</span> <span class="nf">christmas</span>
<span class="c">% Anselm Ivanovas, anselm.ivanovas@student.unisg.ch</span>
<span class="c">%Basically just a nice plot for some christmas fun.</span>
<span class="c">%3D Plot of a hhristmas tree with some presents and snow</span>
<span class="c">%% setup</span>
<span class="n">snow</span><span class="p">=</span><span class="mi">800</span><span class="p">;</span> <span class="c">% number of snow flakes [0 .. 5000]</span>

<span class="c">%% draw tree</span>
<span class="n">h</span><span class="p">=</span><span class="mi">0</span><span class="p">:</span><span class="mf">0.2</span><span class="p">:</span><span class="mi">25</span><span class="p">;</span> <span class="c">%vertical grid</span>
<span class="p">[</span><span class="n">X</span><span class="p">,</span><span class="n">Y</span><span class="p">,</span><span class="n">Z</span><span class="p">]</span> <span class="p">=</span> <span class="n">cylinder</span><span class="p">(</span><span class="n">tree</span><span class="p">(</span><span class="n">h</span><span class="p">));</span> <span class="c">%produce a tree formed cylinder</span>
<span class="n">Z</span><span class="p">=</span><span class="n">Z</span><span class="o">*</span><span class="mi">25</span><span class="p">;</span> <span class="c">%scale to the right heigth</span>
<span class="c">%add some diffusion to the surface of the tree to make it look more real</span>
<span class="n">treeDiffusion</span><span class="p">=</span><span class="nb">rand</span><span class="p">(</span><span class="mi">126</span><span class="p">,</span><span class="mi">21</span><span class="p">)</span><span class="o">-</span><span class="mf">0.5</span><span class="p">;</span><span class="c">%some horizontal diffusion data</span>
<span class="c">%add diffusion to the grid points</span>
<span class="k">for</span> <span class="n">cnt1</span><span class="p">=</span><span class="mi">1</span><span class="p">:</span><span class="mi">21</span>

<span class="k">for</span> <span class="n">cnt2</span><span class="p">=</span><span class="mi">16</span><span class="p">:</span><span class="mi">126</span><span class="c">%starting above the trunk</span>
<span class="c">%get the angle to always diffuse in direction of the radius</span>
<span class="nb">angle</span><span class="p">=</span><span class="nb">atan</span><span class="p">(</span><span class="n">Y</span><span class="p">(</span><span class="n">cnt2</span><span class="p">,</span><span class="n">cnt1</span><span class="p">)</span><span class="o">/</span><span class="n">X</span><span class="p">(</span><span class="n">cnt2</span><span class="p">,</span><span class="n">cnt1</span><span class="p">));</span>
<span class="c">%split the diffusion in the two coordinates, depending on the angle</span>
<span class="n">X</span><span class="p">(</span><span class="n">cnt2</span><span class="p">,</span><span class="n">cnt1</span><span class="p">)=</span><span class="n">X</span><span class="p">(</span><span class="n">cnt2</span><span class="p">,</span><span class="n">cnt1</span><span class="p">)</span><span class="o">+</span><span class="nb">cos</span><span class="p">(</span><span class="nb">angle</span><span class="p">)</span><span class="o">*</span><span class="n">treeDiffusion</span><span class="p">(</span><span class="n">cnt2</span><span class="p">,</span><span class="n">cnt1</span><span class="p">);</span>
<span class="n">Y</span><span class="p">(</span><span class="n">cnt2</span><span class="p">,</span><span class="n">cnt1</span><span class="p">)=</span><span class="n">Y</span><span class="p">(</span><span class="n">cnt2</span><span class="p">,</span><span class="n">cnt1</span><span class="p">)</span><span class="o">+</span><span class="nb">sin</span><span class="p">(</span><span class="nb">angle</span><span class="p">)</span><span class="o">*</span><span class="n">treeDiffusion</span><span class="p">(</span><span class="n">cnt2</span><span class="p">,</span><span class="n">cnt1</span><span class="p">);</span>
<span class="c">%some Vertical diffusion for each point</span>
<span class="n">Z</span><span class="p">(</span><span class="n">cnt2</span><span class="p">,</span><span class="n">cnt1</span><span class="p">)=</span><span class="n">Z</span><span class="p">(</span><span class="n">cnt2</span><span class="p">,</span><span class="n">cnt1</span><span class="p">)</span><span class="o">+</span><span class="p">(</span><span class="nb">rand</span><span class="o">-</span><span class="mf">0.5</span><span class="p">)</span><span class="o">*</span><span class="mf">0.5</span><span class="p">;</span>
<span class="k">end</span>

<span class="k">end</span>
<span class="c">%draw the tree</span>
<span class="n">surfl</span><span class="p">(</span><span class="n">X</span><span class="p">,</span><span class="n">Y</span><span class="p">,</span><span class="n">Z</span><span class="p">,</span><span class="s">'light'</span><span class="p">)</span>
<span class="c">%% View and format</span>
<span class="c">%Use as nice green color map (darker at the bottom, lighter at the top)</span>
<span class="n">r</span><span class="p">=(</span><span class="mf">0.0430</span><span class="p">:(</span><span class="mf">0.2061</span><span class="o">/</span><span class="mi">50</span><span class="p">):</span><span class="mf">0.2491</span><span class="p">)</span><span class="o">'</span><span class="p">;</span><span class="c">%red component</span>
<span class="n">g</span><span class="p">=(</span><span class="mf">0.2969</span><span class="p">:(</span><span class="mf">0.4012</span><span class="o">/</span><span class="mi">50</span><span class="p">):</span><span class="mf">0.6981</span><span class="p">)</span><span class="o">'</span><span class="p">;</span><span class="c">%green component</span>
<span class="n">b</span><span class="p">=(</span><span class="mf">0.0625</span><span class="p">:(</span><span class="mf">0.2696</span><span class="o">/</span><span class="mi">50</span><span class="p">):</span><span class="mf">0.3321</span><span class="p">)</span><span class="o">'</span><span class="p">;</span><span class="c">%blue component</span>
<span class="n">map</span><span class="p">=[</span><span class="n">r</span><span class="p">,</span><span class="n">g</span><span class="p">,</span><span class="n">b</span><span class="p">];</span><span class="c">%join in a map</span>
<span class="k">for</span> <span class="n">cnt</span><span class="p">=</span><span class="mi">1</span><span class="p">:</span><span class="mi">6</span>
<span class="c">%change the lower part to brown for the trunk</span>
<span class="n">map</span><span class="p">(</span><span class="n">cnt</span><span class="p">,:)=[</span><span class="mi">77</span><span class="p">,</span><span class="mi">63</span><span class="p">,</span><span class="mi">5</span><span class="p">]</span><span class="o">/</span><span class="mi">265</span><span class="p">;</span>
<span class="k">end</span>
<span class="n">colormap</span><span class="p">(</span><span class="n">map</span><span class="p">)</span><span class="c">%set the map</span>
<span class="n">view</span><span class="p">([</span><span class="o">-</span><span class="mf">37.5</span><span class="p">,</span><span class="mi">4</span><span class="p">])</span><span class="c">%Change the view to see a little more of the Actual 3D tree</span>
<span class="n">lighting</span> <span class="n">phong</span> <span class="c">%some nice lighting</span>
<span class="n">shading</span> <span class="n">interp</span> <span class="c">%remove grid and smoothen the surface color</span>
<span class="n">axis</span> <span class="n">equal</span> <span class="c">%takes care of display in the right proportion</span>
<span class="n">axis</span><span class="p">([</span><span class="o">-</span><span class="mi">10</span> <span class="mi">10</span> <span class="o">-</span><span class="mi">10</span> <span class="mi">10</span> <span class="mi">0</span> <span class="mi">30</span><span class="p">])</span> <span class="c">%give some more axis space (for the snow later)</span>
<span class="n">axis</span> <span class="n">off</span> <span class="c">%but don't show axis</span>
<span class="n">hold</span> <span class="n">on</span> <span class="c">%to draw the rest</span>
<span class="n">title</span><span class="p">(</span><span class="s">'Merry Christmas 知乎er'</span><span class="p">)</span><span class="c">%self explaining</span>
<span class="c">%% Presents</span>
<span class="c">%Draw some presents around the tree (each with random color)</span>
<span class="n">drawPresent</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="o">-</span><span class="mi">4</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">2</span><span class="p">);</span>
<span class="n">drawPresent</span><span class="p">(</span><span class="o">-</span><span class="mi">4</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mf">1.5</span><span class="p">);</span>
<span class="n">drawPresent</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">);</span>
<span class="n">drawPresent</span><span class="p">(</span><span class="o">-</span><span class="mi">14</span><span class="p">,</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">6</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">);</span>
<span class="n">drawPresent</span><span class="p">(</span><span class="o">-</span><span class="mi">9</span><span class="p">,</span><span class="o">-</span><span class="mi">10</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</span><span class="p">);</span>
<span class="n">drawPresent</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">4</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">);</span>
<span class="n">drawPresent</span><span class="p">(</span><span class="o">-</span><span class="mi">6</span><span class="p">,</span><span class="o">-</span><span class="mi">13</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">);</span>
<span class="c">%% Snow</span>
<span class="c">%create some random 3D coordinates for the snow (amount as in setup above)</span>
<span class="n">snowX</span><span class="p">=(</span><span class="nb">rand</span><span class="p">(</span><span class="n">snow</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="mi">25</span><span class="o">-</span><span class="mf">12.5</span><span class="p">);</span>
<span class="n">snowY</span><span class="p">=(</span><span class="nb">rand</span><span class="p">(</span><span class="n">snow</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="mi">25</span><span class="o">-</span><span class="mf">12.5</span><span class="p">);</span>
<span class="n">snowZ</span><span class="p">=(</span><span class="nb">rand</span><span class="p">(</span><span class="n">snow</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span><span class="o">*</span><span class="mi">27</span><span class="p">);</span>
<span class="c">%Note:Some flakes will end up IN the tree but just can't be seen then</span>
<span class="n">plot3</span><span class="p">(</span><span class="n">snowX</span><span class="p">,</span><span class="n">snowY</span><span class="p">,</span><span class="n">snowZ</span><span class="p">,</span><span class="s">'w*'</span><span class="p">)</span><span class="c">%plot coordinates as white snow flakes</span>
<span class="n">hold</span> <span class="n">off</span><span class="c">%Done</span>
<span class="k">end</span> <span class="c">% of function</span>

<span class="c">%% ============= private functions</span>
<span class="k">function</span><span class="w"> </span>r<span class="p">=</span><span class="nf">tree</span><span class="p">(</span>h<span class="p">)</span><span class="c">%Gives a profile for the tree</span>
<span class="k">for</span> <span class="n">cnt</span><span class="p">=</span><span class="mi">1</span><span class="p">:</span><span class="nb">length</span><span class="p">(</span><span class="n">h</span><span class="p">)</span>

<span class="k">if</span><span class="p">(</span><span class="n">h</span><span class="p">(</span><span class="n">cnt</span><span class="p">)</span><span class="o">==</span><span class="mi">0</span><span class="p">)</span><span class="c">%no Width at the bottom. Ensures a "closed" trunk</span>
<span class="n">r</span><span class="p">(</span><span class="n">cnt</span><span class="p">)=</span><span class="mi">0</span><span class="p">;</span>
<span class="k">end</span>
<span class="c">%smaller radius for the trunk</span>
<span class="k">if</span> <span class="p">(</span><span class="n">h</span><span class="p">(</span><span class="n">cnt</span><span class="p">)</span><span class="o">></span><span class="mi">0</span> <span class="o">&&</span> <span class="n">h</span><span class="p">(</span><span class="n">cnt</span><span class="p">)</span><span class="o"><</span><span class="p">=</span><span class="mi">3</span><span class="p">)</span>
<span class="n">r</span><span class="p">(</span><span class="n">cnt</span><span class="p">)=</span><span class="mf">1.5</span><span class="p">;</span>
<span class="k">end</span>
<span class="c">%reduce radius gradually from 8 to 0. Note: will only work with a trunk heigth</span>
<span class="c">%of 3 and a whole tree heigth of 25. Scale the height of the tree in</span>
<span class="c">%the "draw tree" section, since the cylinder command will return a 1</span>
<span class="c">%unit high cylinder anyway</span>
<span class="k">if</span><span class="p">(</span><span class="n">h</span><span class="p">(</span><span class="n">cnt</span><span class="p">)</span><span class="o">></span><span class="mi">3</span><span class="p">)</span>
<span class="n">r</span><span class="p">(</span><span class="n">cnt</span><span class="p">)=</span><span class="mi">8</span><span class="o">-</span><span class="p">(</span><span class="n">h</span><span class="p">(</span><span class="n">cnt</span><span class="p">)</span><span class="o">-</span><span class="mi">3</span><span class="p">)</span><span class="o">*</span><span class="mf">0.3636</span><span class="p">;</span>
<span class="k">end</span>
<span class="k">end</span>
<span class="k">end</span> <span class="c">% of function</span>
<span class="c">%Draws a present with the given coordinate + size in a random color</span>
<span class="c">%Note:Given coordinates apply to the lower front + left corner of the</span>
<span class="c">%present (the one closest to the viewer) as seen in the plot</span>
<span class="k">function</span><span class="w"> </span><span class="nf">drawPresent</span><span class="p">(</span>dx,dy,dz,scalex,scaley,scalez<span class="p">)</span><span class="w"></span>
<span class="c">%the standard present coordinates</span>
<span class="n">presentX</span><span class="p">=[</span><span class="mf">0.5</span> <span class="mf">0.5</span> <span class="mf">0.5</span> <span class="mf">0.5</span> <span class="mf">0.5</span><span class="p">;</span> <span class="mi">0</span> <span class="mi">1</span> <span class="mi">1</span> <span class="mi">0</span> <span class="mi">0</span><span class="p">;</span> <span class="mi">0</span> <span class="mi">1</span> <span class="mi">1</span> <span class="mi">0</span> <span class="mi">0</span><span class="p">;</span> <span class="mi">0</span> <span class="mi">1</span> <span class="mi">1</span> <span class="mi">0</span> <span class="mi">0</span><span class="p">;</span> <span class="mf">0.5</span> <span class="mf">0.5</span> <span class="mf">0.5</span> <span class="mf">0.5</span> <span class="mf">0.5</span><span class="p">];</span>
<span class="n">presentY</span><span class="p">=[</span><span class="mf">0.5</span> <span class="mf">0.5</span> <span class="mf">0.5</span> <span class="mf">0.5</span> <span class="mf">0.5</span><span class="p">;</span> <span class="mi">0</span> <span class="mi">0</span> <span class="mi">1</span> <span class="mi">1</span> <span class="mi">0</span><span class="p">;</span> <span class="mi">0</span> <span class="mi">0</span> <span class="mi">1</span> <span class="mi">1</span> <span class="mi">0</span><span class="p">;</span> <span class="mi">0</span> <span class="mi">0</span> <span class="mi">1</span> <span class="mi">1</span> <span class="mi">0</span><span class="p">;</span> <span class="mf">0.5</span> <span class="mf">0.5</span> <span class="mf">0.5</span> <span class="mf">0.5</span> <span class="mf">0.5</span><span class="p">];</span>
<span class="n">presentZ</span><span class="p">=[</span><span class="mi">0</span> <span class="mi">0</span> <span class="mi">0</span> <span class="mi">0</span> <span class="mi">0</span><span class="p">;</span> <span class="mi">0</span> <span class="mi">0</span> <span class="mi">0</span> <span class="mi">0</span> <span class="mi">0</span><span class="p">;</span> <span class="mf">0.5</span> <span class="mf">0.5</span> <span class="mf">0.5</span> <span class="mf">0.5</span> <span class="mf">0.5</span><span class="p">;</span> <span class="mi">1</span> <span class="mi">1</span> <span class="mi">1</span> <span class="mi">1</span> <span class="mi">1</span><span class="p">;</span> <span class="mi">1</span> <span class="mi">1</span> <span class="mi">1</span> <span class="mi">1</span> <span class="mi">1</span><span class="p">];</span>
<span class="c">%draw some presents with random colors</span>
<span class="c">%scale present and move it to the right place and get the plot handle</span>
<span class="n">myHandle</span><span class="p">=</span><span class="n">surf</span><span class="p">((</span><span class="n">presentX</span><span class="o">*</span><span class="n">scalex</span><span class="o">+</span><span class="n">dx</span><span class="p">),(</span><span class="n">presentY</span><span class="o">*</span><span class="n">scaley</span><span class="o">+</span><span class="n">dy</span><span class="p">),</span> <span class="p">(</span><span class="n">presentZ</span><span class="o">*</span><span class="n">scalez</span><span class="o">+</span><span class="n">dz</span><span class="p">));</span>
<span class="c">%some random color map</span>
<span class="n">randColorMap</span><span class="p">(:,:,</span><span class="mi">1</span><span class="p">)=</span><span class="nb">repmat</span><span class="p">(</span><span class="nb">rand</span><span class="p">,[</span><span class="mi">5</span><span class="p">,</span><span class="mi">5</span><span class="p">]);</span><span class="c">%r component</span>
<span class="n">randColorMap</span><span class="p">(:,:,</span><span class="mi">2</span><span class="p">)=</span><span class="nb">repmat</span><span class="p">(</span><span class="nb">rand</span><span class="p">,[</span><span class="mi">5</span><span class="p">,</span><span class="mi">5</span><span class="p">]);</span><span class="c">%g component</span>
<span class="n">randColorMap</span><span class="p">(:,:,</span><span class="mi">3</span><span class="p">)=</span><span class="nb">repmat</span><span class="p">(</span><span class="nb">rand</span><span class="p">,[</span><span class="mi">5</span><span class="p">,</span><span class="mi">5</span><span class="p">]);</span><span class="c">%b component</span>
<span class="c">%Assign colormap just to the plot handle object of the present, so the tree</span>
<span class="c">%does not change color</span>
<span class="n">set</span><span class="p">(</span><span class="n">myHandle</span><span class="p">,</span><span class="s">'CData'</span><span class="p">,</span><span class="n">randColorMap</span><span class="p">)</span>
<span class="n">shading</span> <span class="n">interp</span> <span class="c">%Nice shding + without grid</span>
<span class="k">end</span> <span class="c">% of function</span>

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Christmas Tree
R语言能画，但是这种比较有什么意义呢..................................

<span class="go">L <-  matrix(</span>
<span class="go">    c(0.03,  0,     0  ,  0.1,</span>
<span class="go">        0.85,  0.00,  0.00, 0.85,</span>
<span class="go">        0.8,   0.00,  0.00, 0.8,</span>
<span class="go">        0.2,  -0.08,  0.15, 0.22,</span>
<span class="go">        -0.2,   0.08,  0.15, 0.22,</span>
<span class="go">        0.25, -0.1,   0.12, 0.25,</span>
<span class="go">        -0.2,   0.1,   0.12, 0.2),</span>
<span class="go">    nrow=4)</span>
<span class="go"># ... and each row is a translation vector</span>
<span class="go">B <- matrix(</span>
<span class="go">    c(0, 0,</span>
<span class="go">        0, 1.5,</span>
<span class="go">        0, 1.5,</span>
<span class="go">        0, 0.85,</span>
<span class="go">        0, 0.85,</span>
<span class="go">        0, 0.3,</span>
<span class="go">        0, 0.4),</span>
<span class="go">    nrow=2)</span>

<span class="go">prob = c(0.02, 0.6,.08, 0.07, 0.07, 0.07, 0.07)</span>

<span class="go"># Iterate the discrete stochastic map </span>
<span class="go">N = 1e5 #5  #   number of iterations </span>
<span class="go">x = matrix(NA,nrow=2,ncol=N)</span>
<span class="go">x[,1] = c(0,2)   # initial point</span>
<span class="go">k <- sample(1:7,N,prob,replace=TRUE) # values 1-7 </span>

<span class="go">for (i in 2:N) </span>
<span class="go">  x[,i] = crossprod(matrix(L[,k[i]],nrow=2),x[,i-1]) + B[,k[i]] # iterate </span>

<span class="go"># Plot the iteration history </span>
<span class="go">png('card.png')</span>
<span class="go">par(bg='darkblue',mar=rep(0,4))    </span>
<span class="go">plot(x=x[1,],y=x[2,],</span>
<span class="go">    col=grep('green',colors(),value=TRUE),</span>
<span class="go">    axes=FALSE,</span>
<span class="go">    cex=.1,</span>
<span class="go">    xlab='',</span>
<span class="go">    ylab='' )#,pch='.')</span>

<span class="go">bals <- sample(N,20)</span>
<span class="go">points(x=x[1,bals],y=x[2,bals]-.1,</span>
<span class="go">    col=c('red','blue','yellow','orange'),</span>
<span class="go">    cex=2,</span>
<span class="go">    pch=19</span>
<span class="go">)</span>
<span class="go">text(x=-.7,y=8,</span>
<span class="go">    labels='Merry',</span>
<span class="go">    adj=c(.5,.5),</span>
<span class="go">    srt=45,</span>
<span class="go">    vfont=c('script','plain'),</span>
<span class="go">    cex=3,</span>
<span class="go">    col='gold'</span>
<span class="go">)</span>
<span class="go">text(x=0.7,y=8,</span>
<span class="go">    labels='Christmas',</span>
<span class="go">    adj=c(.5,.5),</span>
<span class="go">    srt=-45,</span>
<span class="go">    vfont=c('script','plain'),</span>
<span class="go">    cex=3,</span>
<span class="go">    col='gold'</span>
<span class="go">)</span>
<span class="go">dev.off()</span>
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