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I was asked how to do this today and thought that I would share the answer:
## Sample points uniformly within a fixed radius

nrand=1000
maxstep=10

## Sample data
## NB: To get a truly uniform sample over the circle, you must
##     sample the square of the distance and then transform back.
tempdat<-data.frame(X0=0,Y0=0, bearing0=0,
dist2=sqrt(runif(nrand)*maxstep^2),
turningangle=runif(nrand)*2*pi-pi)

##convert Turning angle to bearing (in this case no change)
tempdat$bearing=tempdat$bearing0+tempdat$turningangle ## Convert from polar to cartesian coordinates tempdat$X<-tempdat$X0+tempdat$dist2*sin(tempdat$bearing) tempdat$Y<-tempdat$Y0+tempdat$dist2*cos(tempdat$bearing) tempdat$Xbad<-tempdat$X0+tempdat$bad.dist*sin(tempdat$bearing) tempdat$Ybad<-tempdat$Y0+tempdat$bad.dist*cos(tempdat\$bearing)

##make plots
png(filename="sampleplots.png",width=500,height=1000)
par(mfrow=c(2,1))