Rotation of Basic Shapes 3

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def rotate_xy(k,x,y):

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    return [[(cos(i*pi/k)*x-sin(i*pi/k)*y).n(),

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             (sin(i*pi/k)*x+cos(i*pi/k)*y).n()] 

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            for i in range(2*k)]

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def shape_mandala(k,n,m):

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    centers=[rotate_xy(n,.5+k*i,.5+k*i) 

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             for i in range(m)] 

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    r=[randint(300,1800)/1000 for i in range(m)]

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    col=[[randint(300,900)/1000 

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          for j in range(2)]+[1] for i in range(m)]

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    p=sum([sum([polygon(

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        [[x+cos(pi*j/i),y+sin(pi*j/i)] for j in range(2*i)],

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        color=col[m-i-1],fill=False,thickness=.7) 

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                for [x,y] in centers[i]]) for i in [m-3,m-5]])

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    el=sum([sum([ellipse(

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        [x,y],r[i],r[m-i-1],arctan(y/x),facecolor=col[i],

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        fill=True,alpha=.05)+\

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       ellipse([x,y],r[i],r[m-i-1],arctan(y/x),

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               color=col[m-i-1],thickness=.7) 

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                 for [x,y] in centers[i]]) for i in [m-2,m-4]])

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    c=sum([sum([circle(

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        [x,y],r[i],facecolor=col[i],fill=True,alpha=.05)+\

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       circle([x,y],r[i],color=col[m-i-1],thickness=.7) 

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                for [x,y] in centers[i]]) 

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           for i in list(range(m-5))+[m-1]])

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    (p+el+c).show(axes=false,figsize=9,

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                  title=r'$k=%.3f; \ m=%d; \ n=%d$'%(k,m,n))

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k,n,m=randint(100,900)/1000,randint(5,15),randint(7,12); 

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shape_mandala(k,n,m)

Language: Sage Gap GP HTML Macaulay2 Maxima Octave Python R Singular

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