Visualization Notes: 12/11/19

Wednesday, December 11, 2019

Polygon Plotting with Random Coefficients 3

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r.svg(filename='"Rplots.svg"',width=6,height=6,onefile=True,
    family='"times"',bg='"black"',pointsize=10,
    antialias=r.c('"default"','"none"','"gray"','"subpixel"'))
r.eval("""
a<-sample(5:11,1); b<-sample(13:19,1)
c<-2*sample(3:10,1); n<-sample(18:144,1)
t<-seq(1,2*n+1,.1)
col=rgb(runif(1),runif(1),1,alpha=.3)
plot(0,0,type='n',xlim=c(-3,3),ylim=c(-3,3))
for (k in 1:c){
    fx<-sin(pi*t/n+k*2*pi/c)-
        sin(a*pi*t/n+k*2*pi/c)+sin(b*pi*t/n+k*2*pi/c)
    fy<-cos(pi*t/n+k*2*pi/c)+
        cos(a*pi*t/n+k*2*pi/c)+cos(b*pi*t/n+k*2*pi/c)
    polygon(fx,fy,lwd=1.5,border=col,xlab='',ylab='',
            xlim=c(-3,3),ylim=c(-3,3))
    par(new=TRUE)}
paste0('a = ',a,'; b = ',b,'; c = ',c,'; n = ',n)
""")
r.dev_off()

Polygon Plotting with Random Coefficients 2

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r.svg(filename='"Rplots.svg"',width=6,height=6,onefile=True,
    family='"courier"',bg='"oldlace"',pointsize=10,
    antialias=r.c('"default"','"none"','"gray"','"subpixel"'))
r.eval("""
a<-sample(5:11,1); b<-sample(13:19,1)
c<-2*sample(3:10,1); n<-sample(18:144,1)
t<-seq(1,2*n+1,2)
col=rgb(runif(1),runif(1),1,alpha=.3)
plot(0,0,type='n',xlim=c(-3,3),ylim=c(-3,3),
     xaxt='n',yaxt='n',xlab='',ylab='',frame=FALSE)
for (k in 1:c){
    fx<-sin(pi*t/n+k*2*pi/c)-
        sin(a*pi*t/n+k*2*pi/c)+sin(b*pi*t/n+k*2*pi/c)
    fy<-cos(pi*t/n+k*2*pi/c)+
        cos(a*pi*t/n+k*2*pi/c)+cos(b*pi*t/n+k*2*pi/c)
    polygon(fx,fy,lwd=1,xaxt='n',yaxt='n',frame=FALSE,
            border=rgb(1,runif(1),runif(1),alpha=.8),
            xlab='',ylab='',xlim=c(-3,3),ylim=c(-3,3))
    par(new=TRUE)}
paste0('a = ',a,'; b = ',b,'; c = ',c,'; n = ',n)
""")
r.dev_off()

Polygon Plotting with Random Coefficients

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r.svg(filename='"Rplots.svg"',width=6,height=6,onefile=True,
    family='"sans"',bg='"black"',pointsize=10,
    antialias=r.c('"default"','"none"','"gray"','"subpixel"'))
r.eval("""
a<-sample(5:11,1); b<-sample(13:19,1)
c<-2*sample(3:10,1); n<-sample(18:36,1)
t<-seq(1,2*n+1,1); col=rgb(runif(1),1,runif(1),alpha=.1)
plot(0,0,type='n',xlim=c(-3,3),ylim=c(-3,3))
for (k in 1:c){
    fx<-sin(pi*t/n+k*2*pi/c)-
        sin(a*pi*t/n+k*2*pi/c)+sin(b*pi*t/n+k*2*pi/c)
    fy<-cos(pi*t/n+k*2*pi/c)+
        cos(a*pi*t/n+k*2*pi/c)+cos(b*pi*t/n+k*2*pi/c)
    polygon(fx,fy,lwd=.01,col=col,xlab='',ylab='',
            xlim=c(-3,3),ylim=c(-3,3)); par(new=TRUE)}
paste0('a = ',a,'; b = ',b,'; c = ',c,'; n = ',n)
""")
r.dev_off()

Plotting with Random Coefficients

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r.svg(filename='"Rplots.svg"',width=6,height=6,onefile=True,
    family='"sans"',bg='"ivory"',pointsize=10,
    antialias=r.c('"default"','"none"','"gray"','"subpixel"'))
r.eval("""
a<-sample(5:11,1); b<-sample(13:19,1); c<-2*sample(3:6,1)
n<-sample(18:36,1); t<-seq(1,2*n+1,.1)
fx0<-sin(pi*t/n)-sin(a*pi*t/n)+sin(b*pi*t/n)
fy0<-cos(pi*t/n)+cos(a*pi*t/n)+cos(b*pi*t/n)
for (k in 1:c){
    fx<-sin(pi*t/n+k*2*pi/c)-sin(a*pi*t/n+k*2*pi/c)+
        sin(b*pi*t/n+k*2*pi/c)
    fy<-cos(pi*t/n+k*2*pi/c)+cos(a*pi*t/n+k*2*pi/c)+
        cos(b*pi*t/n+k*2*pi/c)
    plot(fx,fy,type='o',cex=.1,lwd=.5,
         col=rgb(1-.4*runif(1),.5*runif(1),0),
         xlab='',ylab='',xlim=c(-3,3),ylim=c(-3,3))
    par(new=TRUE)}
plot(fx0,fy0,type='o',cex=.2,lwd=10,
     col=rgb(1-.4*runif(1),.5*runif(1),0,alpha=.05),
     xlab='x',ylab='y',xlim=c(-3,3),ylim=c(-3,3))
grid(col='slategray')
paste0('a = ',a,'; b = ',b,'; c = ',c,'; n = ',n)
""")
r.dev_off()

A Fun App with Several Code Lines 2

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el=['😸','😹','😻','😼','😽','😾','😿','🙀']
var('t,k'); n=randint(16,36)
a,b,c=randint(5,12),randint(13,24),2*randint(3,6)
st1='<p style="font-size:190%; color:'
st2='">=>Fortune Telling on a Chamomile</p>'
def col(): 
    return Color(1,random(),random()).html_color()
pretty_print(html(st1+col()+st2))
fy(t,k)=cos(pi*t/n+2*k*pi/c)
fy(t,k)=fy(t,k)+cos(a*pi*t/n+2*k*pi/c)+\
        cos(b*pi*t/n+2*k*pi/c)
fx(t,k)=sin(pi*t/n+2*k*pi/c)
fx(t,k)=fx(t,k)-sin(a*pi*t/n+2*k*pi/c)+\
        sin(b*pi*t/n+2*k*pi/c)
L=[[[fx(t,k),fy(t,k)] 
    for t in range(2*n)] for k in range(2*c)]
sum([polygon2d(L[i],color=col(),thickness=.5,
               alpha=.1,axes=False) 
     for i in range(2*c)])+text(el[randint(0,len(el)-1)],
     (0,0),fontsize=120,color=col())

A Fun App with Several Code Lines

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el=['😀','😁','😂','😃','😄','😅','😆','😇','😈','😉',
    '😊','😋','😌','😍','😎','😏','😐','😑','😒','😓',
    '😔','😕','😖','😗','😘','😙','😚','😛','😜','😝',
    '😞','😟','😠','😡','😢','😣','😥','😦','😧','😨',
    '😩','😪','😫','😭','😮','😯','😰','😱','😲','😳',
    '😴','😵','😶','😷']
st1='<p style="color:#aa00ff; font-size:150%;'+\
    ' padding:0px 0px 0px 70px;">'
st2='$\\mathbb{Emotional \\; Horoscope \\; '+\
    'of \\; the \\; Day}$</p>'
pretty_print(html(st1+st2))
var('t,k'); n=randint(16,36)
a,b,c=randint(5,11),randint(12,24),2*randint(3,6)
fy(t,k)=cos(pi*t/n+2*k*pi/c)
fy(t,k)=fy(t,k)+cos(a*pi*t/n+2*k*pi/c)+\
        cos(b*pi*t/n+2*k*pi/c)
fx(t,k)=sin(pi*t/n+2*k*pi/c)
fx(t,k)=fx(t,k)-sin(a*pi*t/n+2*k*pi/c)+\
        sin(b*pi*t/n+2*k*pi/c)
L=[[[fx(t,k),fy(t,k)] 
    for t in range(2*n)] for k in range(2*c)]
EL=[(3*cos(j*pi/12),3*sin(j*pi/12)) for j in [1..24]]
def col(): return (random(),0,random())
EP1=sum([polygon2d(L[i],color=col(),
                   thickness=.7,alpha=.05) 
         for i in range(2*c)])
EP2=sum([text(el[randint(0,len(el)-1)]+' '+str(31-j),EL[j-1],
              fontsize=16,color=col()) for j in [7..24]])
EP3=text(el[randint(0,len(el)-1)],(0,0),
         fontsize=100,color='#aa00ff')
(EP1+EP2+EP3).show(axes=False,figsize=(6,6))

Rotations of Graph Plots 2

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def krotate_graph(g):
    G=Graphics(); nv=list(g.get_pos().keys())
    n=len(nv); v=g.get_pos().values()
    k=randint(3,12); pretty_print('k = %d'%k)
    for i in range(2*k):
        a=i*pi/k
        col=colormaps.prism(randint(10,250))         
        va=[[(.3*k*cos(a)*x-sin(a)*y).n(),
             (.3*k*sin(a)*x+cos(a)*y).n()] 
            for [x,y] in v]
        da=dict((nv[i],va[i]) 
                for i in range(n))
        G+=g.graphplot(
            pos=da,edge_color=col[:3],edge_thickness=.7,
            vertex_labels=False,vertex_size=0).plot()
    G.show(axes=False,figsize=6)
krotate_graph(graphs.CubeGraph(3))

Rotations of Graph Plots

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def col(): 
    return [.01*randint(30,90) for i in range(3)]
def rotate_graph(g,k):
    G=Graphics(); nv=list(g.get_pos().keys())
    n=len(nv); v=g.get_pos().values() 
    for i in range(2*k):
        a=i*pi/k
        va=[[(cos(a)*x-sin(a)*y).n(),
             (sin(a)*x+cos(a)*y).n()] 
            for [x,y] in v]
        da=dict((nv[i],va[i]) for i in range(n))
        G+=g.graphplot(
            pos=da,edge_color=col(),edge_thickness=.7,
            vertex_labels=False,vertex_size=0).plot()
    G.show(axes=False,figsize=7)
rotate_graph(graphs.CubeGraph(4),9)

Transformations of Polar Plots

PPRT[n_,col_,l_,s_]:=Module[{a,b,c,d,u},
u=Pi/n; a=RandomInteger[{4,12}]; b=RandomInteger[{12,18}];
c=RandomInteger[{25,81}]; d=RandomInteger[{216,256}];
PF1[i_,t_]:=(a+.9Cos[b*t+u*i])(1+.1Cos[c*t+u*i]);
PF2[i_,t_]:=(1+.05Cos[d*t+u*i])(1+Sin[t+u*i]);
Show[Table[PolarPlot[PF1[i,t]*PF2[i,t],{t,-Pi,Pi},
PlotStyle->{Thickness[l],ColorData[col][.1Mod[i,Floor[n/2]]]}],
{i,2n+1}],Axes->False,ImageSize->s,PlotPoints->50]]
{PPRT[16,"BrightBands",.01,300],PPRT[4,"Rainbow",.001,300]}

PPRT[8,"CherryTones",0,600]

RotationTransform - Pattern Array Examples

AGRTP[m_,k_,s_,col_]:=Module[{ag},
ag=AdjacencyGraph[ExampleData[

{"Matrix",ExampleData["Matrix"][[m,2]]},"Matrix"]["PatternArray"],

DirectedEdges->False,VertexSize->0];
CS[i_]:=ColorData[col][6Mod[i,Round[k/6]]/k];
RTAG[i_]:=RotationTransform[

2i*Pi/k,{0,0}]/@ResourceFunction["VertexCoordinateList"][ag]//N;
Show[Table[GraphPlot[ag,

VertexCoordinates->RTAG[i],EdgeStyle->CS[i]],{i,k}],ImageSize->s]]
{AGRTP[277,30,300,"CherryTones"],

AGRTP[420,24,300,"CoffeeTones"]}

AGRTP[269,24,600,"CandyColors"]

RotationTransform - 3D Graph Examples

RTPT[poly_,n_,d_,p_,s_]:=Graphics3D[

Table[Tube[RotationTransform[i*Pi/n,{0,0,1},
p]/@PolyhedronData[poly,"Edges","Coordinates"],d],{i,2n}],
Boxed->False,ViewPoint->Top,

Background->Black,ImageSize->s];
{RTPT["EscherSolid",8,.02,{1.2,1.2,1.2},300],
RTPT["Dodecahedron",8,.07,{1,1,1},300]}

RTPT["GyroelongatedPentagonalBirotunda",

4,.02,{1.3,1.3,1.3},600]

RotationTransform - Graph Examples

LFG[g_,n_,s_]:=Module[{edges,vertices,rtv},
edges=GraphData[g,"Edges"];

vertices=GraphData[g,"VertexCoordinates"];
rtv=Table[RotationTransform[j*Pi/n,{1.3,1.3}]/@vertices,{j,2n}];
lt[j_]:=Table[{rtv[[j]][[edges[[i,1]]]],
rtv[[j]][[edges[[i,2]]]]},{i,Length[edges]}];
Graphics[Table[Line[lt[j]],{j,2n}],ImageSize->s]]
{LFG["HundredTwentyCellGraph",3,300],

LFG["DoubleStarSnark",9,300]}

LFG["SixHundredCellGraph",4,900]

Relief Plotting for Complex Functions

RPC1[m_,n_,s_,col_]:=With[{z=x+I y},ReliefPlot[Table[Cos[m*#]*Sin[#],
{x,##2},{y,##2}]&[If[Abs[z]>1.1 ,0,#]&@Arg[Sum[(z^n+10^(-3)z)^k!,{k,4}]],
-1.11,1.11,.005],ImageSize->s,ColorFunction->col]];
{RPC1[81,8,300,"GrayTones"],RPC1[64,5,300,"CherryTones"]}

RPC2[m_,n_,col_]:=With[{z=x+I y},ReliefPlot[Table[Cos[m*#],
{x,##2},{y,##2}]&[If[Abs[z]>1.15 ,0,#]&@Arg[Sum[(Sin[3z]*z)^k!,{k,4}]],
-1.2,1.2,.005],ImageSize->600,ColorFunction->col]];
RPC2[81,8,"BrassTones"]