#----------------------------#
#                            #
#    Loesungen UeBlatt13     #
#                            #
#----------------------------#


# Aufgabe 1:

ramp = colorRamp( c("white","black") )    
ramp    
 
ramp( seq(0,1,length = 100) )            
                                          
rgb( ramp(seq(0,1,length = 100)) , max=255 )    

mycol = rgb( ramp(seq(0,1,length = 100)) , max=255 )
mycol


# check:

n = 100
sigma = seq(from = 1/2, to = 2, length=n)
x = seq(from = -10, to=10, by=0.01)

plot(x , dnorm(x,mean=0,sd=sigma[1]) )
for(i in 2:n)
{
  points(x, dnorm(x,mean=0,sd=sigma[i]), col = mycol[i] )     
}


# Image-Plot Random-Potential:

M = 100
N = 200
lattice = t(outer(1:N,1i*(1:M),FUN="+"))          
donors = sample(lattice,N*M/100,replace=FALSE)    

RandPot = matrix(0,nrow=M,ncol=N)
for(donor in donors)
{
  distances = sqrt(abs(lattice-donor)^2 + 15) 
  RandPot = RandPot + 1/distances^3
}

par(pin=c(6,6*M/N))
image(1:N, 1:M, t(RandPot), main="Random Potential", col=mycol ,xlab="" )
image(1:N, 1:M, t(RandPot), main="Random Potential", col=rev(mycol) ,xlab="" )





# Aufgabe 2


# eine Farbpalette von weiss nach gelb:

ramp1 = colorRamp(c("white","yellow"))      
ramp1                                     

mycol1 = rgb( ramp1(seq(0,1,length = 100) ), max = 255)
mycol1                                   

# quick check:
n = 100
sigma = seq(from = 1/2, to = 2, length=n)
plot(x , dnorm(x,mean=0,sd=sigma[1]) )
for(i in 2:n)
{
  points(x, dnorm(x,mean=0,sd=sigma[i]), col = mycol1[i] )     
}
# soweit ok


# eine Farbpalette von blau nach schwarz:

ramp2 = colorRamp(c("blue","black"))      
ramp2                                     

mycol2 = rgb( ramp2(seq(0,1,length = 100) ), max = 255)
mycol2                                   

# quick check:
n = 100
plot(x , dnorm(x,mean=0,sd=sigma[1]) )
for(i in 2:n)
{
  points(x, dnorm(x,mean=0,sd=sigma[i]), col = mycol2[i] )     
}
# soweit ok


# rainbow()-Palette, eingeschraenkt auf das Intervall [gelb,blau]:
# mit etwas probieren findet man die Grenzen fuer start und end:

mycol0 = rainbow(500, start=1/6, end=4/6 )
mycol0

# quick check:
n = 500
sigma = seq(from = 1/2, to = 2, length=n)
plot(x , dnorm(x,mean=0,sd=sigma[1]) )
for(i in 2:n)
{
  points(x, dnorm(x,mean=0,sd=sigma[i]), col = mycol0[i] )     
}
# soweit ok


# Jetzt packen wir alles zusammen: 

mycol = c( mycol1 , mycol0 , mycol2 )    


# check:
n = 700
sigma = seq(from = 1/2, to = 2, length=n)
plot(x , dnorm(x,mean=0,sd=sigma[1]) )
for(i in 2:n)
{
  points(x, dnorm(x,mean=0,sd=sigma[i]), col = mycol[i] )     
}

# das passt 



# Image-Plot Random-Potential:

M = 100
N = 200
lattice = t(outer(1:N,1i*(1:M),FUN="+"))          
donors = sample(lattice,N*M/100,replace=FALSE)    

RandPot = matrix(0,nrow=M,ncol=N)
for(donor in donors)
{
  distances = sqrt(abs(lattice-donor)^2 + 15) 
  RandPot = RandPot + 1/distances^3
}

par(pin=c(6,6*M/N))
image(1:N, 1:M, t(RandPot), main="Random Potential", col=mycol ,xlab="" )
image(1:N, 1:M, t(RandPot), main="Random Potential", col=rev(mycol) ,xlab="" )