如何用數學軟體畫一個「聖誕樹」?

01-07

可以是字元的，也可以是圖形的
相關問題如何用C語言畫一個「聖誕樹」? - 編程

我只是搬運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]

（原圖是動圖，傳上知乎後不能動了）原出處：popularity contest

Wolfram Mathematica 算數學軟體吧？

還有這個：

算不算抖機靈 = =

Mathematica版本：

打開一個notebook，然後長按CTRL+/,效果如下：

像不像一棵聖誕樹呢？

這裡有用SAS畫的聖誕樹，翻譯成了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]

能畫。

去年用R畫了聖誕樹送給教定量入門的教授，改了一下Wiekvoet: Merry Christmas的代碼。

（今年直接手動塗色送happy spring的卡片了，不是程序媛搞不出酷炫的東西好桑心）

MATLAB ，名副其實的數學軟體。

參考 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

雞汁的我

Making a Christmas Animation with the Wolfram Mathematica

Christmas Tree

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