# Code to view correlation in pseudorandom numbers generated by a LCG
# David Read, California State University, Easy Bay, 3/30/09

library(rgl)

# Note: This is a TERRIBLE LCG used only to show the correlation. 

N=26

Seed       = 44
Mvalue     = 26
Cvalue     = 27
Dvalue     = 3
v1         = numeric(N)
v1[1]      = Seed
for (i in 2:N)
	{Next = (Cvalue*Seed + Dvalue)%%Mvalue
       v1[i] = Next
       Seed = Next
      }

v2<-v1/Mvalue

plot(v2[1:(N-1)], v2[2:N], main="Correlation of Pseudorandom Numbers from a Linear Congruential Generator")

# Note: This LCG has passed, and still passes, many tests for "randomness" 
#       and is suggested for use by the U.S. Bureau of Standards in 1964. 

N=100000

Seed       = 762939453125                           	
Mvalue     = 2^47
Cvalue     = (2^7)+1
Dvalue     = 29741096258473
v1         = numeric(N)
v1[1]      = Seed
for (i in 2:N)
	{Next = (Cvalue*Seed + Dvalue)%%Mvalue
       v1[i] = Next
       Seed = Next
      }

v2<-v1/Mvalue

# View correlation in 2-dimensions. X-axis is v[i-1], Y-axis is v[i]. 
# Expand this image to full screen to see the "structure." 

plot(v2[1:(N-1)], v2[2:N], main="Correlation of Pseudorandom Numbers from a Linear Congruential Generator")

# View correlation in 3-dimensions. X-axis is v[i-2], Y-axis is v[i-1], 
# Z-axis is v[i]. 
# NOTE: You MUST install and load the R package rgl for this code to work. 
# The 3d image can be rotated by clicking and dragging. The mouse wheel zooms. 
# The "structure" can be seen by rotating the image until the empty planes can
# be seen. Again, full screen is best. 

plot3d(v2[1:(N-2)], v2[2:(N-1)], v2[3:N], main="Correlation of Pseudorandom Numbers from a Linear Congruential Generator")