library(ggplot2) get_path <- function(x_start,time_end){ out <- c(rnorm(1,x_start,1)) for(time in c(2:time_end)){ out <- c(out, rnorm(1,out[time-1],1)) } return(out) } time_end <- 1e3 x_start <- 0 n_process <- 100 path_store <- c() for(process in c(1:n_process)){ path_store <- rbind(path_store, cbind(rep(process, time_end), c(1:time_end), get_path(x_start,time_end))) } path_store <- data.frame(process=path_store[,1], time=path_store[,2], path=path_store[,3]) ggplot(path_store, aes(time, path, group=process, col=process)) + geom_path() + theme_classic() + theme(legend.position="none") + theme(axis.title.x=element_blank(), axis.text.x=element_blank(), axis.ticks.x=element_blank(), axis.title.y=element_blank(), axis.text.y=element_blank(), axis.ticks.y=element_blank())