├── README.md
├── LICENSE
└── mondrianomies.R


/README.md:
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 1 | # The Mondrianomies
 2 | 
 3 | This project creates images like this, inspired in neoplasticism based on L-Systems:
 4 | 
 5 | <img src="https://fronkonstin.com/wp-content/uploads/2022/03/dkzwov.png?resize=1024%2C1024&ssl=1" width="800" align="middle">
 6 | 
 7 | ## Getting Started
 8 | 
 9 | ### Prerequisites
10 | 
11 | You will need to install the following packages (if you don't have them already):
12 | 
13 | ```
14 | install.packages("gsubfn")
15 | install.packages("tidyverse")
16 | ```
17 | 
18 | ## More info
19 | 
20 | The code is simple and is implemented in R.
21 | 
22 | A complete explanation of the experiment can be found [at fronkonstin](https://fronkonstin.com/2022/03/25/the-mondrianomies/)
23 | 
24 | ## Authors
25 | 
26 | * **Antonio Sánchez Chinchón** - [@aschinchon](https://twitter.com/aschinchon)
27 | 
28 | 


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/LICENSE:
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 1 | MIT License
 2 | 
 3 | Copyright (c) 2022 Antonio Sánchez Chinchón
 4 | 
 5 | Permission is hereby granted, free of charge, to any person obtaining a copy
 6 | of this software and associated documentation files (the "Software"), to deal
 7 | in the Software without restriction, including without limitation the rights
 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 9 | copies of the Software, and to permit persons to whom the Software is
10 | furnished to do so, subject to the following conditions:
11 | 
12 | The above copyright notice and this permission notice shall be included in all
13 | copies or substantial portions of the Software.
14 | 
15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
21 | SOFTWARE.
22 | 


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/mondrianomies.R:
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  1 | ####################################################################
  2 | library(gsubfn)
  3 | library(tidyverse)
  4 | 
  5 | # Number of symbols in rule
  6 | s <- sample(15:26, 1) 
  7 | # Extract s symbols from c("F", "+", "-") randomly
  8 | v1 <- sample(c("F", "+", "-"), size = s, replace = TRUE, prob = c(10,12,12))
  9 | # Add 3 pairs of brackets
 10 | v2 <- sample("[]", 3, replace = TRUE) %>% str_extract_all("\\d*\\+|\\d*\\-|F|L|R|\\[|\\]|\\|") %>% unlist
 11 | # Where to insert brackets
 12 | v3 <- sample(1:(s+1), size = length(v2)) %>% sort
 13 | # Insert them correctly
 14 | for(i in 1:length(v3)){
 15 |   c(v1[1:(v3[i] + i - 1)], v2[i], v1[(v3[i] + i - 1):length(v1)]) -> v1
 16 | }
 17 | 
 18 | # All ictures start with the same axiom
 19 | axiom <- "F-F-F-F"
 20 | # Rule to substitute F, as generated previously
 21 | rules <- list("F"=paste(v1, collapse=""))
 22 | # Turning angle
 23 | angle <- 90
 24 | # Haw many times to apply the rule
 25 | depth <- sample(3:4,1)
 26 | # Longitude (factor) of the segments
 27 | ds <- jitter(1)
 28 | # Substitute axiom depth times
 29 | for (i in 1:depth) axiom <- gsubfn(".", rules, axiom)
 30 | # Actions that will gneerate the drawing  
 31 | actions <- str_extract_all(axiom, "\\d*\\+|\\d*\\-|F|L|G|R|\\[|\\]|\\|") %>% unlist
 32 |   
 33 | # These vars store the current position, angle and longitude factor of the point
 34 | x_current <- 0
 35 | y_current <- 0
 36 | a_current <- 0
 37 | d_current <- 0
 38 | 
 39 | # To store point position, angle and longitude
 40 | status <- tibble(x = x_current, 
 41 |                  y = y_current, 
 42 |                  alfa = a_current,
 43 |                  depth = d_current)
 44 | # To store segments  
 45 | lines <- data.frame(x = numeric(), 
 46 |                     y = numeric(), 
 47 |                     xend = numeric(), 
 48 |                     yend = numeric())
 49 | 
 50 | # This loop reads actions and generates the drawing depending on the concrete action
 51 | #   F -> draw forward
 52 | #   + -> turn right
 53 | #   - -> turn left
 54 | #   [ -> save the current status of point
 55 | #   ] -> restore the last current status of point and remove from stack
 56 | for (action in actions) 
 57 | {
 58 |   if (action=="F") {
 59 |     lines <- lines %>% add_row(x = x_current,
 60 |                                y = y_current,
 61 |                                xend = x_current + (ds^d_current) * cos(a_current * pi / 180),
 62 |                                yend = y_current + (ds^d_current) * sin(a_current * pi / 180)) 
 63 |     x_current <- x_current + (ds^d_current) * cos(a_current * pi / 180)
 64 |     y_current <- y_current + (ds^d_current) * sin(a_current * pi / 180)
 65 |     d_current <- d_current + 1
 66 |   }
 67 |   if (action=="+") {
 68 |     a_current <- a_current - angle
 69 |   }
 70 |   if (action=="-") {
 71 |     a_current <- a_current + angle
 72 |   }
 73 |   if (action=="[") { 
 74 |     status <- status %>% add_row(x = x_current, 
 75 |                                  y = y_current, 
 76 |                                  alfa = a_current,
 77 |                                  depth = d_current)
 78 |   }
 79 |   if (action=="]") {
 80 |     x_current <- tail(status, 1) %>% pull(x)
 81 |     y_current <- tail(status, 1) %>% pull(y)
 82 |     a_current <- tail(status, 1) %>% pull(alfa)
 83 |     d_current <- tail(status, 1) %>% pull(depth)
 84 |     status <- head(status, -1)
 85 |   }
 86 | }
 87 | 
 88 |   lines %>%
 89 |     mutate(x = round(x, 1),
 90 |            y = round(y, 1),
 91 |            xend = round(xend, 1),
 92 |            yend = round(yend, 1)) %>%
 93 |     distinct(x, y, xend, yend) -> lines
 94 |   
 95 |   select(lines, x3 = x, y3 =y) %>%
 96 |     bind_rows(select(lines, x3 = xend, y3 =yend)) %>%
 97 |     distinct(x3, y3) -> points
 98 |   
 99 | # Let's find squares to fill inside the drawing
100 | # Since this operation maybe hard to compute, I divide points into 
101 | # 10 pieces to process them separately
102 | n <- 10
103 |   
104 | split(points, rep(1:ceiling(nrow(points)/n), 
105 |                   each = n, 
106 |                   length.out = nrow(points))) -> points_divided
107 |   
108 | # Squares1: add X3, y3 to current segments and filter to find 
109 | # right angles
110 |   lapply(points_divided, function(sub) {
111 |     sub %>% 
112 |       crossing(lines) %>%
113 |       filter(x == x3 | y == y3 | xend == x3 | yend == y3) %>%
114 |       filter(x != x3 | y != y3 , xend != x3 | yend != y3) %>%
115 |       mutate(id = row_number())
116 |   }) %>% bind_rows() -> squares1
117 |   
118 | # Squares2:  keep those squares where some of new sides exist in lines
119 | bind_rows(
120 |     squares1 %>%
121 |       inner_join(lines, c("x" = "x", 
122 |                           "y" = "y", 
123 |                           "x3" = "xend", 
124 |                           "y3" = "yend")),
125 |     squares1 %>%
126 |       inner_join(lines, c("xend" = "x", 
127 |                           "yend" = "y", 
128 |                           "x3" = "xend", 
129 |                           "y3" = "yend")),
130 |     squares1 %>%
131 |       inner_join(lines, c("x3" = "x", 
132 |                           "y3" = "y", 
133 |                           "x" = "xend", 
134 |                           "y" = "yend")),
135 |     squares1 %>%
136 |       inner_join(lines, c("x3" = "x", 
137 |                           "y3" = "y", 
138 |                           "xend" = "xend", 
139 |                           "yend" = "yend"))) %>%
140 |     distinct(x, y, xend, yend, x3, y3, id) -> squares2
141 |   
142 | # Remove those whose sides form a straight line
143 | squares2 %>% 
144 |     anti_join(squares2 %>% filter(x == xend, xend == x3),
145 |               by = c("x", "y", "xend", "yend", "x3", "y3", "id")) -> squares2
146 |   
147 | squares2 %>% 
148 |     anti_join(squares2 %>% filter(y == yend, yend == y3),
149 |               by = c("x", "y", "xend", "yend", "x3", "y3", "id")) -> squares2
150 |   
151 | # We leave squares2 prepared for geom_rect
152 | squares2 %>%
153 |     mutate(xmax = pmax(x, xend, x3),
154 |            xmin = pmin(x, xend, x3),
155 |            ymax = pmax(y, yend, y3),
156 |            ymin = pmin(y, yend, y3)) %>%
157 |     mutate(A = (xmax - xmin) * (ymax - ymin) / 2) -> squares
158 |   
159 | # Piet mondrian's palette
160 | colors <- c("#FEFFFA","#000002","#F60201","#FDED01", "#1F7FC9")
161 | 
162 | # To remove very small squares I calculate quantiles form its area
163 | qnts <- quantile(squares$A, 
164 |                    probs = seq(0, 1, 0.05), 
165 |                    na.rm = FALSE,
166 |                    names = TRUE, 
167 |                    type = 7)
168 | 
169 | # Here comes the magic of ggplot
170 | ggplot() +
171 |     geom_rect(aes(xmax = xmax,
172 |                   xmin = xmin,
173 |                   ymax = ymax,
174 |                   ymin = ymin,
175 |                   fill = id %% length(colors) %>% jitter(amount=.025)),
176 |               data = squares %>% filter(A >= qnts[1]), # remove small squares
177 |               lwd = 2,
178 |               color = "white") +
179 |     geom_segment(aes(x = x, y = y, xend = xend, yend = yend),
180 |                  data = lines,
181 |                  lwd = .65,
182 |                  lineend = "square",
183 |                  color = "#000002") +
184 |     scale_fill_gradientn(colors = colors) +
185 |     theme_void() +
186 |     theme(legend.position = "none") +
187 |     coord_equal() -> plot
188 |   
189 | # Calculate dimensions of the picture for ggsave
190 | width <- max(points$x3) - min(points$x3)
191 | height <- max(points$y3) - min(points$y3)
192 |   
193 | whmax <- 8
194 | if (width >= height) {
195 |   w <- whmax
196 |   h <- whmax * height / width 
197 | } else {
198 |   h <- whmax
199 |     w <- whmax * width / height
200 | }
201 |   
202 | # Save the drawing with a random name
203 | name <- paste(sample(letters,6), collapse = "")
204 | ggsave(paste0("new/",name,".png"), plot, width = w, height = h)
205 |   
206 | 
207 | 
208 |   
209 | 
210 | 


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