如何用数学软件画一个“圣诞树”?

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

回复内容：我只是搬运 http:// codegolf.stackexchange测试数据上的答案，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]

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？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]

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。
参考参考 File Exchange
by Anselm Ivanovas
====================================
%
function christmas % Anselm Ivanovas, anselm.ivanovas@student.unisg.ch %Basically just a nice plot for some christmas fun. %3D Plot of a hhristmas tree with some presents and snow %% setup snow = 800 ; % number of snow flakes [0 .. 5000] %% draw tree h = 0 : 0.2 : 25 ; %vertical grid [ X , Y , Z ] = cylinder ( tree ( h )); %produce a tree formed cylinder Z = Z * 25 ; %scale to the right heigth %add some diffusion to the surface of the tree to make it look more real treeDiffusion = rand ( 126 , 21 ) - 0.5 ; %some horizontal diffusion data %add diffusion to the grid points for cnt1 = 1 : 21 for cnt2 = 16 : 126 %starting above the trunk %get the angle to always diffuse in direction of the radius angle = atan ( Y ( cnt2 , cnt1 ) / X ( cnt2 , cnt1 )); %split the diffusion in the two coordinates, depending on the angle X ( cnt2 , cnt1 )= X ( cnt2 , cnt1 ) + cos ( angle ) * treeDiffusion ( cnt2 , cnt1 ); Y ( cnt2 , cnt1 )= Y ( cnt2 , cnt1 ) + sin ( angle ) * treeDiffusion ( cnt2 , cnt1 ); %some Vertical diffusion for each point Z ( cnt2 , cnt1 )= Z ( cnt2 , cnt1 ) + ( rand - 0.5 ) * 0.5 ; end end %draw the tree surfl ( X , Y , Z , 'light' ) %% View and format %Use as nice green color map (darker at the bottom, lighter at the top) r =( 0.0430 :( 0.2061 / 50 ): 0.2491 ) ' ; %red component g =( 0.2969 :( 0.4012 / 50 ): 0.6981 ) ' ; %green component b =( 0.0625 :( 0.2696 / 50 ): 0.3321 ) ' ; %blue component map =[ r , g , b ]; %join in a map for cnt = 1 : 6 %change the lower part to brown for the trunk map ( cnt ,:)=[ 77 , 63 , 5 ] / 265 ; end colormap ( map ) %set the map view ([ - 37.5 , 4 ]) %Change the view to see a little more of the Actual 3D tree lighting phong %some nice lighting shading interp %remove grid and smoothen the surface color axis equal %takes care of display in the right proportion axis ([ - 10 10 - 10 10 0 30 ]) %give some more axis space (for the snow later) axis off %but don't show axis hold on %to draw the rest title ( 'Merry Christmas 知乎er' ) %self explaining %% Presents %Draw some presents around the tree (each with random color) drawPresent ( 2 , - 4 , 0 , 3 , 3 , 2 ); drawPresent ( - 4 , 3 , 0 , 2 , 3 , 1.5 ); drawPresent ( 5 , 3 , 0 , 4 , 3 , 3 ); drawPresent ( - 14 , - 5 , 0 , 6 , 3 , 1 ); drawPresent ( - 9 , - 10 , 0 , 2 , 2 , 2 ); drawPresent ( 0 , 4 , 0 , 4 , 3 , 3 ); drawPresent ( - 6 , - 13 , 0 , 3 , 3 , 3 ); %% Snow %create some random 3D coordinates for the snow (amount as in setup above) snowX =( rand ( snow , 1 ) * 25 - 12.5 ); snowY =( rand ( snow , 1 ) * 25 - 12.5 ); snowZ =( rand ( snow , 1 ) * 27 ); %Note:Some flakes will end up IN the tree but just can't be seen then plot3 ( snowX , snowY , snowZ , 'w*' ) %plot coordinates as white snow flakes hold off %Done end % of function %% ============= private functions function r = tree ( h ) %Gives a profile for the tree for cnt = 1 : length ( h ) if ( h ( cnt ) == 0 ) %no Width at the bottom. Ensures a "closed" trunk r ( cnt )= 0 ; end %smaller radius for the trunk if ( h ( cnt ) > 0 && h ( cnt ) = 3 ) r ( cnt )= 1.5 ; end %reduce radius gradually from 8 to 0. Note: will only work with a trunk heigth %of 3 and a whole tree heigth of 25. Scale the height of the tree in %the "draw tree" section, since the cylinder command will return a 1 %unit high cylinder anyway if ( h ( cnt ) > 3 ) r ( cnt )= 8 - ( h ( cnt ) - 3 ) * 0.3636 ; end end end % of function %Draws a present with the given coordinate + size in a random color %Note:Given coordinates apply to the lower front + left corner of the %present (the one closest to the viewer) as seen in the plot function drawPresent ( dx,dy,dz,scalex,scaley,scalez ) %the standard present coordinates presentX =[ 0.5 0.5 0.5 0.5 0.5 ; 0 1 1 0 0 ; 0 1 1 0 0 ; 0 1 1 0 0 ; 0.5 0.5 0.5 0.5 0.5 ]; presentY =[ 0.5 0.5 0.5 0.5 0.5 ; 0 0 1 1 0 ; 0 0 1 1 0 ; 0 0 1 1 0 ; 0.5 0.5 0.5 0.5 0.5 ]; presentZ =[ 0 0 0 0 0 ; 0 0 0 0 0 ; 0.5 0.5 0.5 0.5 0.5 ; 1 1 1 1 1 ; 1 1 1 1 1 ]; %draw some presents with random colors %scale present and move it to the right place and get the plot handle myHandle = surf (( presentX * scalex + dx ),( presentY * scaley + dy ), ( presentZ * scalez + dz )); %some random color map randColorMap (:,:, 1 )= repmat ( rand ,[ 5 , 5 ]); %r component randColorMap (:,:, 2 )= repmat ( rand ,[ 5 , 5 ]); %g component randColorMap (:,:, 3 )= repmat ( rand ,[ 5 , 5 ]); %b component %Assign colormap just to the plot handle object of the present, so the tree %does not change color set ( myHandle , 'CData' , randColorMap ) shading interp %Nice shding + without grid end % of function
Christmas Tree
R语言能画，但是这种比较有什么意义呢..................................

L c(0.03, 0, 0 , 0.1, 0.85, 0.00, 0.00, 0.85, 0.8, 0.00, 0.00, 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), nrow=4) # ... and each row is a translation vector B c(0, 0, 0, 1.5, 0, 1.5, 0, 0.85, 0, 0.85, 0, 0.3, 0, 0.4), nrow=2) prob = c(0.02, 0.6,.08, 0.07, 0.07, 0.07, 0.07) # Iterate the discrete stochastic map N = 1e5 #5 # number of iterations x = matrix(NA,nrow=2,ncol=N) x[,1] = c(0,2) # initial point k for (i in 2:N) x[,i] = crossprod(matrix(L[,k[i]],nrow=2),x[,i-1]) + B[,k[i]] # iterate # Plot the iteration history png('card.png') par(bg='darkblue',mar=rep(0,4)) plot(x=x[1,],y=x[2,], col=grep('green',colors(),value=TRUE), axes=FALSE, cex=.1, xlab='', ylab='' )#,pch='.') bals points(x=x[1,bals],y=x[2,bals]-.1, col=c('red','blue','yellow','orange'), cex=2, pch=19 ) text(x=-.7,y=8, labels='Merry', adj=c(.5,.5), srt=45, vfont=c('script','plain'), cex=3, col='gold' ) text(x=0.7,y=8, labels='Christmas', adj=c(.5,.5), srt=-45, vfont=c('script','plain'), cex=3, col='gold' ) dev.off()

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更新时间：2022-10-19 阅读：42次