This small generative art project uses code from my previous work. I really liked the looped path objects and decided to try something else with them. This work expands the loop a little, adds a randomly generated color scheme, and uses a standard image style.
Code
The first function is get_maze. This code creates a maze from a size-by-size grid. The final code uses a base size of ten. The maze starts at the bottom middle and randomly adds edges.
[get_maze function]
get_maze <-function(size) {# Sets up base data set of potential edges for the maze# size is always 5 for right now edges <-CJ(x1 =rep(seq(1, size), 2),y1 =seq(1, size) ) edges[, ":="(x2 =ifelse(.I %%2==0, x1 +1, x1),y2 =ifelse(.I %%2==1, y1 +1, y1))] edges <- edges[x2 <= size & y2 <= size, ] edges[, id :=seq(1, nrow(edges))] edges[, ":="(node1 = (x1 -1) * size + (y1 -1) +1,node2 = (x2 -1) * size + (y2 -1) +1)]setkey(edges, id)# data set of nodes nodes <-unique(rbind(edges[, .(id = node1)], edges[, .(id = node2)])) nodes[, connected :=0]setkey(nodes, id)# data set of node id to edge ids nodes_edges <-unique(rbind(edges[, .(id = node1, edge = id)][], edges[, .(id = node2, edge = id)]))setkey(nodes_edges, id)# location : 1 for maze, 0 for frontier, -1 for uncharted, -2 for discarded# starting point : bottom middle# include bottom middle then either off to the sides or up starting_edge <- edges[(x1 ==3& y1 ==1) | (x1 ==2& y1 ==1& x2 ==3& y2 ==1), ][sample(.N, 1), ]# Set up base columns edges[, ":="(location =-1,probability =0)] edges[.(starting_edge$id), ":="(location =1,probability =0)] nodes[.(c(starting_edge$node1, starting_edge$node2)), connected :=1] edges[.(nodes_edges[.(c(starting_edge$node1, starting_edge$node2)), "edge"]), ":=" (location =fifelse(location ==-1, 0, location),probability =fifelse(location ==-1, 1, probability))]#### Loop through maze generation ---- num_edges <-1while (num_edges < (size^2-1)) {# select next edge selected_edge <- edges[sample(.N, 1, prob = probability), ]## if it's good, then# add it to the maze# add connecting edges to the frontier# else add it to discardif (any(nodes[.(c(selected_edge$node1, selected_edge$node2)) , connected] ==0)) {# add to maze edges[.(selected_edge$id), ":="(location =1,probability =0)]# update nodes nodes[.(c(selected_edge$node1, selected_edge$node2)), connected :=1]# update frontier edges[.(nodes_edges[.(c(selected_edge$node1, selected_edge$node2)) , "edge"]), ":=" (location =fifelse(location ==-1, 0, location),probability =fifelse(location ==-1, 1, probability))] num_edges <- num_edges +1 } else {# drop from frontier edges[.(selected_edge$id), ":="(location =-2,probability =0)] } }return(edges[location ==1, ])}
The next function, update_maze, doubles the edges so that the maze follows a loop. The new connections trace the outline of the maze. This action mimics exploring the maze and following the path back to the start.
[update_maze function]
update_maze <-function(edges) {# list out all possible edges# (basically same code as setting up the maze)# plus adds edges that stick out on the outside size <-max(edges$x1) +1 all_possible_edges <-CJ(x1 =rep(seq(1, size), 2) -1,y1 =seq(1, size) -1 ) all_possible_edges[, ":="(x2 =ifelse(.I %%2==0, x1 +1, x1),y2 =ifelse(.I %%2==1, y1 +1, y1))] all_possible_edges <- all_possible_edges[(x1 !=0| x2 !=0) & (y1 !=0| y2 !=0), ] edges <- edges[, .(x1, x2, y1, y2, id)]# merge maze and all possible edges to see which ones weren't used all_possible_edges <-merge(all_possible_edges, edges,by =c("x1", "y1", "x2", "y2"),all.x =TRUE )# This function subs in the new edges appropriately# basically, any path edge needs to be updated to two edges so the maze# starts at the bottom middle, travels through the maze, and back to the start create_new_edges <-function(x1, y1, x2, y2, id) {# if no edges, add blockif (is.na(id)) {if (y1 == y2) { # horizontal edgelist(x1_1 =2* x1,y1_1 =2* y1 -1,x2_1 =2* x1,y2_1 =2* y1,x1_2 =2* x2 -1,y1_2 =2* y2 -1,x2_2 =2* x2 -1,y2_2 =2* y2 ) } else { # vertical edgelist(x1_1 =2* x1 -1,y1_1 =2* y1,x2_1 =2* x1,y2_1 =2* y1,x1_2 =2* x2 -1,y1_2 =2* y2 -1,x2_2 =2* x2,y2_2 =2* y2 -1 ) } } else { # has edge, add connectionsif (y1 == y2) { # horizontal edgelist(x1_1 =2* x1,y1_1 =2* y1 -1,x2_1 =2* x2 -1,y2_1 =2* y2 -1,x1_2 =2* x1,y1_2 =2* y1,x2_2 =2* x2 -1,y2_2 =2* y2 ) } else { # vertical edgelist(x1_1 =2* x1 -1,y1_1 =2* y1,x2_1 =2* x2 -1,y2_1 =2* y2 -1,x1_2 =2* x1,y1_2 =2* y1,x2_2 =2* x2,y2_2 =2* y2 -1 ) } } }# fill in blocks and paths all_possible_edges[, c("x1_1", "y1_1", "x2_1", "y2_1","x1_2", "y1_2", "x2_2", "y2_2" ) :=create_new_edges(x1, y1, x2, y2, id), by =seq_len(nrow(all_possible_edges)) ]# clean everything up all_possible_edges[, ":="(x1 =NULL,y1 =NULL,x2 =NULL,y2 =NULL,id =NULL)] all_possible_edges <-melt(all_possible_edges,measure.vars =patterns("x1", "y1", "x2", "y2"),value.name =c("x1", "y1", "x2", "y2") )[, variable :=NULL] all_possible_edges <- all_possible_edges[(x1 >0& y1 >0& x2 < (2* size -1) & y2 < (2* size -1)), ]}
The last external function, maze_to_path, puts all the edges in order from the bottom left corner, traveling through the loop and back to the beginning.
[maze_to_path function]
maze_to_path <-function(edges) {# set up id edges[, id := .I]setkey(edges, id)# set up nodes data set nodes <-unique(rbind(edges[, .(x = x1, y = y1)] , edges[, .(x = x2, y = y2)])) nodes[, id := .I]setkey(nodes, id)# add node ids to edges data set edges <-merge(edges, nodes,by.x =c("x1", "y1"), by.y =c("x", "y"),suffixes =c("", "_node_1"), all.x =TRUE ) edges <-merge(edges, nodes,by.x =c("x2", "y2"), by.y =c("x", "y"),suffixes =c("", "_node_2"), all.x =TRUE )# nodes to edges look up table nodes_edges <-unique(rbind( edges[, .(id = id_node_1, edge = id, connecting_node = id_node_2)], edges[, .(id = id_node_2, edge = id, connecting_node = id_node_1)] ))setkey(nodes_edges, id)# save spot for path path <-vector(mode ="numeric")# variables to keep track of progress through the maze current_node <- nodes[y ==1& x ==1, id] first_node <- current_node# update path path <-append(path, current_node) previous_node <- current_node# keep going to unexplored nodes current_node <- nodes_edges[.(current_node), ][connecting_node != previous_node , connecting_node][1]# continue through the whole pathwhile (current_node != first_node) { path <-append(path, current_node) future_node <- nodes_edges[.(current_node), ][connecting_node != previous_node , connecting_node] previous_node <- current_node current_node <- future_node } path <-data.table(order =seq(1, length(path)),node = path ) path <-merge(path, nodes, by.x =c("node"), by.y =c("id"))}
The main workhorse utilizes the previous functions to get a set of connections.
The color scheme code follows a random circle in the HCL color space. There are ten points equidistant around the circle. Sometimes the first random circle will produce invalid color values. So the code loops until it finds a complete set. The circle’s center is saved and used as a border for the images and fills small circles where the connections meet.
Finally, a sine wave with a random number of waves determines the connections’ sizes.
[generate_output code]
library(data.table)library(ggplot2)source("get_maze.R")source("update_maze.R")source("maze_to_path.R")get_set <-function(size) { set <-get_maze(size) set <-update_maze(set) set <-maze_to_path(set) set[, ":="(x = x - (size + .5),y = y - (size + .5))] set <- set[order(order), ] set[, ':=' (xend =shift(x, type ="lead", fill =1- (size + .5) ),yend =shift(y, type ="lead", fill =1- (size + .5) ))]}# Get color scheme by finding a random circle in HCL color spaceget_colors <-function() {# two random vectors v1 <-runif(3, -1, 1) v2 <-runif(3, -1, 1)# orthogonal v2 <- v2 -c(v1 %*% v2 / v1 %*% v1 ) * v1# unit v1 <- v1 /sqrt(c(v1 %*% v1)) v2 <- v2 /sqrt(c(v2 %*% v2))# random point p <-runif(3, -30, 30) +c(0, 0, 50)# random radius r <-runif(1, 10, 30)# ten points around the circle# need to keep both end points even though they're the same value# for scale_color_gradientn to loop back around t <-seq(0, 2* pi, length.out =11) colors <-data.table(p1 = p[1],p2 = p[2],p3 = p[3],r = r,t = t,v11 = v1[1],v12 = v1[2],v13 = v1[3],v21 = v2[1],v22 = v2[2],v23 = v2[3]) colors[, ':=' (x = p1 + r *cos(t) * v11 + r *sin(t) * v21,y = p2 + r *cos(t) * v12 + r *sin(t) * v22,z = p3 + r *cos(t) * v13 + r *sin(t) * v23)] colors[, ":=" (H = (atan2(y, x) *180/pi) %%360,C =sqrt(x^2+ y^2),L = z)] colors[, ':=' (hex_value =ifelse(L <0| L >100, NA_character_, hcl(H, C, L, fixup =FALSE))), by =seq_len(nrow(colors))]return(colors)}# Sometimes the circle will be out of range,# so try again until all the colors are validget_color_scheme <-function() { colors <-get_colors()while(any(is.na(colors$hex_value))) { colors <-get_colors() }return(colors)}# Create 10 outputsset.seed(10101010)for(i in1:10) { size <-10 set <-get_set(size) colors <-get_color_scheme()# Save center of the circle color_center <-hcl(h = (atan2(colors$p2[1], colors$p1[1]) *180/pi) %%360,c =sqrt(colors$p1[1]^2+ colors$p2[1]^2),l = colors$p3[1]) color_scheme <- colors[["hex_value"]]# Get boundaries of white background square boundaries <-data.table(x =c(min(set$x), max(set$x), max(set$x), min(set$x)),y =c(min(set$y), min(set$y), max(set$y), max(set$y))) boundaries[, ':=' (x = x *1.1,y = y *1.1)]# Set up connections size# order goes from 1 to 400# 400 / waves = num segments per wave waves <-round(runif(1, 70, 130)) offset <-runif(1, 0, 2*pi) set[, size := order /max(order) *2*pi] set[, size := (sin(waves * size + offset) +1) *2.5 ]ggplot() +geom_polygon(data = boundaries,aes(x, y),color ="white",fill ="white") +geom_segment(data = set,aes(x, y,xend = xend, yend = yend, color = order, size = size),alpha = .5,lineend ="round") +geom_segment(data = set,aes(x, y,xend = xend, yend = yend, color = order, size = size /5),alpha =1,lineend ="round") +geom_point(data = set,aes(x, y), color = color_center,size = .5) +scale_color_gradientn(colours = color_scheme) +theme_void() +theme(legend.position ="none") +coord_equal()ggsave(paste0("output/output_", i, ".jpeg"), height =5, width =5, bg = color_center)}
