# flower.R
# Oh joy, a toy!
#
# Calculate an optical illusion of flower. See Figure 1 in 
#   Barrow, Bhavsar, Sonoda: 
#        Minimal spanning trees, filaments and galaxy clustering
#   Mon.Not.R.astr.Soc. (1985),216, p.17-35
#
# Author: Tuomas Rajala <tarajala@maths.jyu.fi>
# 
#  Function:
#          flower()
# parameters:
#   ncircles : number of circles emanating from centre
#   npoints  : number of points to evenly spread on each circle
#   R        : radius of outmost circle
#   skip     : illusion parameter, how many circles to skip before setting a point in same radial angle
#   window   : rectangle window in format c(xmin,xmax,ymin,ymax)          
#   x0 , y0  : the centre
#
#
# Example:
#
# pp<-flower(ncircles=50,npoints=100,skip=1)
# plot(pp$x,pp$y,cex=.5+.1*pp$m,col=rgb(.0-.0*pp$m,runif(pp$n,.1+.8*pp$m,.2+.8*pp$m),.0),pch=19) 
#
###########################################################################

flower<-function(ncircles=20, npoints=100, R=4,skip=1,window=c(0,10,0,10),x0=5,y0=5)
{
    rvec<-seq(0,4,length=ncircles)
    x<-x0
    y<-y0
    t<-0
    m<-0
    for(i in 2:ncircles)
    {
        for(j in 0:(npoints-1))
        {
            angle<-(t+(1+skip)*j)*  2*pi/(npoints*(1+skip))
            x<-c(x, x0+cos(angle)*rvec[i])
            y<-c(y, y0+sin(angle)*rvec[i])
            m<-c(m,i)
        }
        t<-t+1
        if(t>skip) t<-0
    }
    list(x=x,y=y,m=m/max(m),n=length(x))
}



flower.meadow<-function(N=5,Rvec=c(1,1,1,1,1))
{
    for(R in Rvec)
    {
        
        pp<-kukkanen(R=R,ncircles=40,x0=runif(1,0,10),y0=runif(1,0,10))
        plot(pp,cex=.2,pch=19,col=heat.colors(max(pp$m))[pp$m],xlim=c(-4,14),ylim=c(-4,14))
        par(new=T)
    }
    par(new=F)
}


#Test run
#pp<-flower(ncircles=100,npoints=100,skip=1)
#plot(pp$x,pp$y,cex=.5+.1*pp$m,col=rgb(.0-.0*pp$m,runif(pp$n,.1+.8*pp$m,.2+.8*pp$m),.0),pch=19)