🔗Asymptote Gallery Tagged by “Array” #112
đź”—fractales-fig009

Show fractales/fig0090.asy on Github.
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Categories : Surveys | Fractals
Tags : #Fractals | #Recursion | #Transform | #Picture | #Array
size(10cm,0); real a=-1.5, b=2a/3; picture H(pen p=currentpen) { picture H; draw(H,(-a,0)--(a,0)^^(-a,-b)--(-a,b)^^(a,-b)--(a,b),p); return H; } transform sc=scale(0.5); transform[] t={identity(), shift(-a,b)*sc, shift(-a,-b)*sc, shift(a,b)*sc, shift(a,-b)*sc}; picture Hfractal(int n, pen p=currentpen) { picture pic; if(n == 0) return H(p); picture Ht=Hfractal(n-1,p); for (int i=0; i < 5; ++i) add(pic,t[i]*Ht); return pic; } add(Hfractal(4, bp+0.5*red));
đź”—fractales-fig010

Show fractales/fig0100.asy on Github.
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Categories : Surveys | Fractals
Tags : #Fractals | #Recursion | #Transform | #Picture | #Array
size(10cm,0); real a=-1.5, b=2a/3; path[] H=(-a,0)--(a,0)^^(-a,-b)--(-a,b)^^(a,-b)--(a,b); transform sc=scale(0.5); transform[] t={shift(-a,b)*sc, shift(-a,-b)*sc, shift(a,b)*sc, shift(a,-b)*sc}; void Hfractal(path[] g, int n, pen[] p=new pen[]{currentpen}) { p.cyclic=true; if(n == 0) draw(H,p[0]); else { for (int i=0; i < 4; ++i) { draw(t[i]*g,p[n]); Hfractal(t[i]*g,n-1,p); } } } Hfractal(H, 5, new pen[] {0.8*red, 0.8*green, 0.8*blue, black, blue+red});
đź”—fractales-fig011

Show fractales/fig0110.asy on Github.
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Categories : Surveys | Fractals
Tags : #Fractals | #Recursion | #Geometry | #Triangle | #Array | #Loop/for/while
import geometry; size(10cm,0); triangle[] dissect(triangle T, int n) { if(n <= 0) return new triangle[]{T}; triangle[] OT; point M=midpoint(T.BC); triangle[] Tp=dissect(triangle(M,T.A,T.B),n-1); for(triangle t : Tp) OT.insert(0,t); triangle[] Tp=dissect(triangle(M,T.C,T.A),n-1); for(triangle t : Tp) OT.insert(0,t); return OT; } triangle T=rotate(45)*triangle((1,1),(0,0),(2,0)); triangle[] DT=dissect(T,9); path g; transform R=reflect(T.BC); for(int i : DT.keys) { draw(DT[i],miterjoin+0.9*red); draw(R*DT[i],miterjoin+0.9*red); g=g--centroid(DT[i]); } draw(scale(sqrt(2))*unitsquare,bp+miterjoin+0.8*blue); draw(g--reverse(R*g)--cycle,bp+miterjoin+yellow); shipout(bbox(sqrt(2)*mm, Fill(black)));
đź”—fractales-fig012

Show fractales/fig0120.asy on Github.
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Categories : Surveys | Fractals
Tags : #Fractals | #Recursion | #Geometry | #Triangle | #Array | #Loop/for/while
size(12cm,0); import geometry; triangle T=triangleAbc(90,Tan(30),1); triangle[] reverse(triangle[] arr) { triangle[] or; int l=arr.length; for(int i=0; i < l; ++i) { or.push(arr[l-i-1]); } return or; } triangle[] dissect(triangle T, int n, bool reverse=false) { if(n <= 0) return new triangle[]{T}; triangle[] OT; point M=curpoint(T.AB,T.b()*Tan(30)); point H=projection(T.BC)*M; triangle[] OT1, OT2, OT3; OT.append(dissect(triangle(H,T.B,M),n-1,!reverse)); OT.append(reverse((dissect(triangle(H,T.C,M),n-1,!reverse)))); OT.append(dissect(triangle(T.A,T.C,M),n-1,!reverse)); return OT; } triangle[] DT=dissect(T,5); point O=centroid(DT[0]); path g; transform Ro=rotate(30,T.B), Re=reflect(T.BC), Roj; for(int i : DT.keys) { O=incenter(DT[i]); g=g--O; } g=reverse(g); path G, g=g--Re*reverse(g) ; for (int j=0; j < 12; j += 2) G=G--Ro^(-j)*g; fill(G--cycle,0.3*blue); for(int i : DT.keys) { for (int j=0; j < 12; j += 2) { Roj=Ro^j; draw(Roj*DT[i],miterjoin+0.8*red); draw(Roj*(Re*DT[i]),miterjoin+0.8*red); } } draw(G--cycle,bp+miterjoin+0.9*yellow); shipout(bbox(2mm, FillDraw(black, 1mm+miterjoin+deepblue)));
đź”—generalities-fig016

Show generalities/fig0160.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Array | #Path
size(6cm, 6cm); pair [] A; A[0]=(-1, -1); A[1]=( 1, -1); A[2]=( 1, 1); A[3]=(-1, 1); draw (A[0]--A[1]--A[2]--A[3]--cycle); draw (A[0]--A[2]); draw (A[1]--A[3]);
đź”—generalities-fig052

Show generalities/fig0520.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Fill/Unfill | #Shading | #Array | #Path
pen[][] p={{rgb(black)}, {rgb(.8red)}}; latticeshade((0,0)--(0,6cm)--(6cm,0)--cycle, p);
đź”—generalities-fig053

Show generalities/fig0530.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Fill/Unfill | #Shading | #Array
pen[][] p={{rgb(black),rgb(black)}, {rgb(red),rgb(green)}}; latticeshade((0,0)--(0,6cm)--(6cm,0)--cycle,p);
đź”—generalities-fig059

Show generalities/fig0590.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Shading | #Tex/latex features | #Texpath | #Fill/Unfill | #Array
size(16cm,0); path[] P=texpath("$\displaystyle\int_{-\infty}^{+\infty}e^{-\alpha x^2}\,dx= \sqrt{\frac{\pi}{\alpha}}$"); pair m=min(P), M=max(P); axialshade(P,yellow,m,red,(m.x,M.y)); draw(P,0.5*blue); shipout(bbox(3mm,Fill));
đź”—generalities-fig101

Show generalities/fig1010.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Circle | #Picture | #Transform/scale/shift/rotate | #Array
size(8cm,0); picture pic; pen [] P={.8red,.7green,blue+.5grey,yellow+.6grey}; fill(scale(10)*unitcircle,.2blue); for (int i = 0; i <= 3; ++i) draw(pic, arc((0,0),10,i*90,(i+1)*90), P[i]); for (real i = 1; i <= 10; i+=.05) add(rotate(90*i)*scale(1/i)*pic);
đź”—generalities-fig154

Show generalities/fig1550.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Array | #Path | #Loop/for/while | #Direction | #Label
size(0,0); pair [] P, Q, R, S; real u=1cm; for (int i=0; i<=4; ++i) P[i] = rotate(i*360/5)*(0,-u); P[5] = P[0]; for (int i=0; i<=4; ++i) Q[i] = 3*midpoint(P[i]--P[i+1]); Q[5] = Q[0]; for (int i=0; i<=4; ++i) R[i] = 1/3*( Q[i] + Q[i+1] + P[i+1] ); R[5] = R[0]; for (int i=0; i<=5; ++i) S[i] = 1.5*Q[i]; for (int i=0; i<=4; ++i) { draw(P[i] -- P[i+1]); draw(P[i+1] -- R[i]); draw(Q[i] -- R[i]); draw(R[i] -- Q[i+1]); draw(Q[i] -- S[i]); draw(S[i] -- S[i+1]); label(format("\small$P_%i$",i),P[i],-unit(P[i])); label(format("\small$Q_%i$",i),Q[i],rotate(60)*unit(Q[i])); label(format("\small$R_%i$",i),R[i],unit(R[i])); label(format("\small$S_%i$",i),S[i],unit(S[i])); }
đź”—generalities-fig155

Show generalities/fig1560.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Array | #Path
size(0,0); pair [] P, Q, R, S; real u=2cm; for (int i=0; i<=4; ++i) P[i] = rotate(i*360/5)*(0,-u); P[5] = P[0]; for (int i=0; i<=4; ++i) Q[i] = 3*midpoint(P[i]--P[i+1]); Q[5] = Q[0]; for (int i=0; i<=4; ++i) R[i] = 1/3*( Q[i] + Q[i+1] + P[i+1] ); R[5] = R[0]; for (int i=0; i<=5; ++i) S[i] = 1.5*Q[i]; for (int i=0; i<=4; ++i) { draw(P[i] -- P[i+1]); draw(P[i+1] -- R[i]); draw(Q[i] -- R[i]); draw(R[i] -- Q[i+1]); draw(Q[i] -- S[i]); draw(S[i] -- S[i+1]); } draw(P[2] -- P[3] -- P[4] -- P[0] -- P[1] -- R[0] -- Q[0] -- R[4] -- Q[4] -- R[3] -- Q[3] -- R[2] -- Q[2] -- S[2] -- S[3] -- S[4] -- S[0] -- S[1] -- Q[1] -- R[1] -- cycle, linewidth(2bp));
đź”—generalities-fig156

Show generalities/fig1570.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Array | #Loop/for/while | #Fill/Unfill | #Shading
size(0,0); pair [] P, Q, R, S; real u=2cm; for (int i=0; i<=4; ++i) P[i] = rotate(i*360/5)*(0,-u); P[5] = P[0]; for (int i=0; i<=4; ++i) Q[i] = 3*midpoint(P[i]--P[i+1]); Q[5] = Q[0]; for (int i=0; i<=4; ++i) R[i] = 1/3*( Q[i] + Q[i+1] + P[i+1] ); R[5] = R[0]; for (int i=0; i<=5; ++i) S[i] = 1.5*Q[i]; fill(shift(-abs(S[0]),-abs(S[0]))*scale(2*abs(S[0]))*unitsquare,.2grey); radialshade(scale(abs(S[0]))*unitcircle,lightgrey,(0,0),abs(S[0]), black,(0,0),abs(.85*midpoint(S[0]--S[1]))); P[6]=P[1]; for (int i=0; i<=4; ++i) { radialshade(S[i]--Q[i]--R[i]--Q[i+1]--S[i+1]--cycle, lightgrey,(0,0),abs(R[i]), black,(0,0),abs(S[i])); radialshade(R[i]--Q[i+1]--R[i+1]--P[i+2]--P[i+1]--cycle, .8red,(0,0),sqrt(1-(2-2cos(pi/5))/4)*u, black,(0,0),abs(Q[i+1])); } for (real i=1; i>0; i-=.05) fill(rotate(90*(1-i))*scale(i)*(P[0]--P[1]--P[2]--P[3]--P[4]--cycle), (1-i)*red); pen p=linewidth(1pt); for (int i=0; i<=4; ++i) { draw(P[i] -- P[i+1],p); draw(P[i+1] -- R[i],p); draw(Q[i] -- R[i],p); draw(R[i] -- Q[i+1],p); draw(Q[i] -- S[i],p); draw(S[i] -- S[i+1],p); } shipout(bbox(0,black+4mm));
đź”—generalities-fig184

Show generalities/fig1860.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Venn diagram | #Path | #Array
// Venn diagram // Diagramme de Venn // Edwards' construction // Construction d'Edwards import roundedpath; size(14cm,0); path [] EdVenn(int n) { path [] opath; if (n>=1) opath.push(shift(-1.4,-.9)*roundedpath(xscale(2.8)*yscale(.9)*unitsquare,.1)); if (n>=2) opath.push(shift(0,-.9)*roundedpath(xscale(1.4)*yscale(1.8)*unitsquare,.1)); if (n>=3) opath.push(scale(.5)*unitcircle); for (int i=1; i<=n-3; ++i) { pair pcle=point(opath[2],1/(2^i)), ccle=intersectionpoint(pcle--(pcle-dir(opath[2],1/(2^i))), (0,0)--(1,0)); path cle=shift(ccle)*scale(abs(pcle-ccle))*unitcircle; real[] p1=intersect(cle, opath[2]); path ocle=subpath(cle,-p1[0],p1[0]); guide tpath; real step=360/(2^i), a=0; for (int j=0; j<2^i; ++j) { tpath=tpath..rotate(a)*ocle; a+=step; } opath.push(tpath..cycle); } return opath; } draw(EdVenn(6));
đź”—generalities-fig188

Show generalities/fig1900.asy on Github.
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Categories : Examples 2D | Generalities
Tags : #Basis | #Path | #Intersection | #Buildcycle | #Transform/scale/shift/rotate | #Array
size(8cm,0); path a,b,c,d; a = (-1,-.2){up} .. tension 1.2 .. (1,-.2){down}; transform r90=rotate(90); b = r90*a; c = r90*b; d = r90*c; path bound=buildcycle(a,b,c,d); fill(bound, lightgrey); draw(a^^b^^c^^d,grey); draw(bound);
đź”—graph-fig025

Show graph/fig0260.asy on Github.
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Categories : Examples 2D | Graph.asy
Tags : #Graph | #Function (drawing) | #Hyperbola | #Contour | #Function (implicit) | #Array
size(10cm,0); import contour; import stats; import graph; xlimits( -5, 5); ylimits( -4, 5); yaxis( "$y$" , Ticks(Label(currentpen+fontsize(8),align=E))); xaxis( "$x$", Ticks(Label(currentpen+fontsize(8)))); real f(real x, real y) {return x^2-x-y^2+3y-6;} int min=-5, max=5, n=max-min+1; real[] value=sequence(min,max); pen[] p=sequence(new pen(int i) { return (value[i] >= 0 ? solid : dashed) + (value[i] >= 0 ? (value[i]/max)*red : (value[i]/min)*blue) + fontsize(4); },n); Label[] Labels=sequence(new Label(int i) { return Label(value[i] != 0 ? (string) value[i] : "",Relative(unitrand()),(0,0), UnFill(1bp)); },n); draw(Labels,contour(f,(-5,-5),(5,5),value),p);
đź”—graph3-fig010

Show graph3/fig0100.asy on Github.
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Categories : Examples 3D | Graph3.asy
Tags : #Graph | #Contour | #Function (implicit) | #Palette | #Axis | #Array
// From documentation of Asymptote import graph; import palette; import contour; texpreamble("\usepackage{icomma}"); size(10cm,10cm,IgnoreAspect); pair a=(0,0); pair b=(5,10); real fz(pair z) { return z.x*z.y*exp(-z.x); } real f(real x, real y) {return fz((x,y));} int N=200; int Divs=10; int divs=2; defaultpen(1bp); pen Tickpen=black; pen tickpen=gray+0.5*linewidth(currentpen); pen[] Palette=BWRainbow(); scale(false); bounds range=image(f,Automatic,a,b,N,Palette); xaxis("$x$",BottomTop,LeftTicks(pTick=grey, ptick=invisible, extend=true)); yaxis("$y$",LeftRight,RightTicks(pTick=grey, ptick=invisible, extend=true)); // Major contours real[] Cvals; Cvals=sequence(11)/10 * (range.max-range.min) + range.min; draw(contour(f,a,b,Cvals,N,operator ..),Tickpen); // Minor contours real[] cvals; real[] sumarr=sequence(1,divs-1)/divs * (range.max-range.min)/Divs; for (int ival=0; ival < Cvals.length-1; ++ival) cvals.append(Cvals[ival]+sumarr); draw(contour(f,a,b,cvals,N,operator ..),tickpen); palette("$f(x,y)=xye^{-x}$",range,point(NW)+(0,1),point(NE)+(0,0.25),Top,Palette, PaletteTicks(N=Divs,n=divs,Tickpen,tickpen));
đź”—graph3-fig015

Show graph3/fig0150.asy on Github.
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Categories : Examples 3D | Graph3.asy
Tags : #Graph (3D) | #Palette | #Surface | #Shading (3D) | #Array | #Spherical harmonics
settings.render=0; import graph3; size(15cm); currentprojection=orthographic(4,2,4); real r(real Theta, real Phi){return 1+0.5*(sin(2*Theta)*sin(2*Phi))^2;} triple f(pair z) {return r(z.x,z.y)*expi(z.x,z.y);} pen[] pens(triple[] z) { return sequence(new pen(int i) { real a=abs(z[i]); return a < 1+1e-3 ? black : interp(blue, red, 2*(a-1)); },z.length); } surface s=surface(f,(0,0),(pi,2pi),100,Spline); // Interpolate the corners, and coloring each patch with one color // produce some artefacts draw(s,pens(s.cornermean())); if(!is3D()) shipout(bbox(3mm,Fill(black)));
đź”—graph3-fig016

Show graph3/fig0160.asy on Github.
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Categories : Examples 3D | Graph3.asy
Tags : #Graph (3D) | #Palette | #Surface | #Shading (3D) | #Array | #Spherical harmonics
settings.render=0; import graph3; size(15cm); currentprojection=orthographic(4,2,4); real r(real Theta, real Phi){return 1+0.5*(sin(2*Theta)*sin(2*Phi))^2;} triple f(pair z) {return r(z.x,z.y)*expi(z.x,z.y);} pen[][] pens(triple[][] z) { pen[][] p=new pen[z.length][]; for(int i=0; i < z.length; ++i) { triple[] zi=z[i]; p[i]=sequence(new pen(int j) { real a=abs(zi[j]); return a < 1+1e-3 ? black : interp(blue, red, 2*(a-1));}, zi.length); } return p; } surface s=surface(f,(0,0),(pi,2pi),100,Spline); // Here we interpolate the pens, this looks smoother, with fewer artifacts draw(s,mean(pens(s.corners()))); if(!is3D()) shipout(bbox(3mm,Fill(black)));
đź”—graph3-fig017

Show graph3/fig0170.asy on Github.
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Categories : Examples 3D | Graph3.asy
Tags : #Graph (3D) | #Palette | #Surface | #Shading (3D) | #Array | #Spherical harmonics
import graph3; size(16cm, 0); currentprojection=orthographic(4, 2, 4); real r(real Theta, real Phi){return 1+0.5*(sin(2*Theta)*sin(2*Phi))^2;} triple f(pair z) {return r(z.x, z.y)*expi(z.x, z.y);} pen[][] pens(triple[][] z) { pen[][] p=new pen[z.length][]; for(int i=0; i < z.length; ++i) { triple[] zi=z[i]; p[i]=sequence(new pen(int j) { real a=abs(zi[j]); return a < 1+1e-3 ? black : interp(blue, red, 2*(a-1));}, zi.length); } return p; } surface s=surface(f, (0, 0), (pi, 2pi), 100, Spline); // Here we determine the colors of vertexes (vertex shading). // Since the PRC output format does not support vertex shading of Bezier surfaces, PRC patches // are shaded with the mean of the four vertex colors. s.colors(pens(s.corners())); draw(s); if(!is3D()) shipout(bbox(1mm, Fill(black)));
đź”—randomwalk-fig001

Show randomwalk/fig0010.asy on Github.
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Categories : Surveys | Random Walk (3D)
Tags : #Random | #Function (creating) | #Array | #Loop/for/while
import three; settings.render=0; // The available directions of steps triple[] dirs={X,-X,Y,-Y,Z,-Z}; dirs.cyclic=true; // Return the nodes of the path triple[] randWalk(real Srnd(), int n) { triple[] randPath; triple camera=1e10*currentprojection.camera; triple pos=O, tpos; int R; for (int i=0; i < n; ++i) { R=round(Srnd()); tpos=pos+dirs[R]; randPath.push(tpos); pos=tpos; } return randPath; } triple[] randWalk(int Srnd(), int n) { real R(){ return Srnd();} return randWalk(R,n); } void drawWalk(triple[] nodes, pen p=white) { triple camera=currentprojection.camera; if(currentprojection.infinity) camera *= max(abs(minbound(nodes)),abs(maxbound(nodes))); real[][] depth; for(int i=0; i < nodes.length-1; ++i) { real d=abs(camera-0.5*(nodes[i]+nodes[i+1])); depth.push(new real[] {d,i}); } depth=sort(depth); triple M=nodes[round(depth[0][1])]; triple m=nodes[round(depth[depth.length-1][1]+1)]; // Draw from farthest to nearest while(depth.length > 0) { real[] a=depth.pop(); int i=round(a[1]); draw(nodes[i]--nodes[i+1],abs(nodes[i]-m)/abs(M-m)*p); } } size(18cm); currentprojection=orthographic((1,1,1)); drawWalk(randWalk(rand,50000),cyan); shipout(bbox(3mm,Fill));
đź”—tube-fig009

Show tube/fig0090.asy on Github.
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Categories : Examples 3D | Tube.asy
Tags : #Tube | #Graph (3D) | #Shading (3D) | #Array
import tube; import graph3; size(10cm,0); currentprojection=perspective(4,3,4); real x(real t) {return (1/sqrt(1+0.5*t^2))*cos(2pi*t);} real y(real t) {return (1/sqrt(1+0.5*t^2))*sin(2pi*t);} real z(real t) {return t;} path3 p=graph(x,y,z,0,2.7,operator ..); path section=scale(0.2)*polygon(4); // Define an array of pen wich depends of a real t. t represent the "reltime" of the path3 p. pen[] pens(real t){ return new pen[] {interp(blue,red,t), interp(orange,yellow,t), interp(green,orange,t), interp(red,purple,t)}; } // "pen[] pens(real t)" allows to color each nodes or segments with a real parameter (the reltime) // Note that all arrays of pens are convert to cyclical arrays. draw(tube(p,coloredpath(section, pens, colortype=coloredNodes)));