Curves and stones

There aren’t many simple geometric objects from cinema that I remember more clearly (and often) than the elemental stones from the Fifth Element movie. I’m trying to flex my skills in procedural art with {ggplot2} and stumbled across this “Waves Patch” piece from Megan Harris’ incredible “rtristy gallery” which inspired me to try and craft something. Let’s give it a go.

Elemental stones from the Fifth Element

“Wave Patch” procedural art by Meghan Harris

Sine curves

Meghan visualises sine curves using by sampling along a sin() curve using seq() and then visualises that curve with geom_path(). Here’s a reproducition of that at it’s simplest:

library("tidyverse")

theta <- seq(from = 0,
             to = 2*pi, 
             length.out = 100)

sine <- tibble(x = theta,
               y = sin(theta),
               label = 1:length(theta))

wave_theta <- seq(from = 0,
                  to = 2 * pi, 
                  by = .1) 

curve_top <- tibble(x = wave_theta,
                    y = sin(x)) %>%
  arrange(x)

curve_top %>%
  ggplot(aes(x=x, y=y))+
  geom_path(arrow = arrow(type="closed"), linewidth = 3) +
  coord_fixed(xlim = c(0, 2 * pi),
              ratio = 1 / 2) +
  theme_void()

Nice! We can stack six of these curves on top of one another using the rep() function.

Side note: do you know the difference between rep() and replicate()? If were interested in adding noise to procedural art replicate() has big advantages we’ll look at in the near future.

wave_theta <- seq(from = 0,
                  to = 2 * pi, 
                  by = .1) 

tibble(x = rep(seq(from = 0,
                  to = 2 * pi, 
                  by = .1) , 6),
       line = rep(1:6, each = length(wave_theta))) %>% 
  mutate(y = line + sin(x),
         line = as.character(line)) %>% 
  ggplot(aes(x=x, y=y, group = line))+
  geom_path(arrow = arrow(type="closed"), linewidth = 5, show.legend = FALSE) +
  scale_x_continuous(expand = expansion(mult = 0, add = c(-0.1, 0.1))) +
  coord_fixed(ratio = 1 / 2) +
  theme_void() +
  theme(panel.background = element_rect(fill = "#9A7D66", colour = "transparent"),
        panel.border = element_blank())

Great! Now to reflect the arrows we need to switch to using a cos() function:

library("patchwork")

gg_L2R_sin_arrowed <- tibble(x = rep(seq(from = 0,
                  to = 2 * pi, 
                  by = .1) , 6),
       line = rep(1:6, each = length(wave_theta))) %>% 
  mutate(y = line + sin(x),
         line = as.character(line)) %>% 
  ggplot(aes(x=x, y=y, group = line))+
  geom_path(arrow = arrow(type="closed", ends = "last"), linewidth = 5, show.legend = FALSE) +
  scale_x_continuous(expand = expansion(mult = 0, add = c(-0.1, 0.1))) +
  scale_y_continuous(expand = expansion(0, c(0.3, 0.3))) +
  coord_fixed(ratio = 1 / 2,
              ylim = c(0, 7)) +
  theme_void() +
  theme(panel.background = element_rect(fill = "#9A7D66", colour = "transparent"),
        panel.border = element_blank()) 

gg_R2L_cos_arrowed <- tibble(x = rep(seq(from = 0,
                  to = 2 * pi, 
                  by = .1) , 6),
       line = rep(-1:4, each = length(wave_theta))) %>% 
  mutate(y = line + cos(x),
         line = as.character(line)) %>% 
  ggplot(aes(x=x, y=y, group = line))+
  geom_path(arrow = arrow(type="closed", ends = "first"), linewidth = 5, show.legend = FALSE) +
  scale_x_continuous(expand = expansion(mult = 0, add = c(0.1, -0.1))) +
  scale_y_continuous(expand = expansion(0, c(0.3, 0.3))) +
  coord_fixed(ratio = 1 / 2,
              ylim = c(-2, 5.2)) +
  theme_void() +
  theme(panel.background = element_rect(fill = "#9A7D66", colour = "transparent"),
        panel.border = element_blank())

ggptch_both_horiz <- gg_L2R_sin_arrowed + theme(plot.margin = margin(r = 10)) | gg_R2L_cos_arrowed

ggptch_both_horiz %>% 
  ggsave(quarto_here("ggptch_both_horiz.png"),
         .,
         width = 5.22 * 2,
         height = 4 )

Arrows in the middle?

It would be a lot more aesthetically pleasing if the direction arrows were in the centre of the image. The easiest way to achieve this is to add geom_segment() into the mix at the centre point with an arrow head. Note that once again we use the geom

seq_x <- seq(from = 0,
                  to = 2 * pi, 
                  by = pi / 100)
n_lines <- 11

data_left_and_right <- tibble(x = rep(seq_x, 9),
       line = rep(seq(-1, 7), each = length(seq_x))) %>% 
  mutate(y = line + sin(x)) 

data_arrows_left_and_right <- data_left_and_right %>% 
  filter(x %in% c(seq_x[c(100, 102)]),
         between(line, 1, 6)) %>% 
  group_by(line) %>%
  summarise(xmin = min(x),
        xmax = max(x),
        ymax = max(y),
        ymin = min(y))

data_left_and_right %>%
  ggplot(aes(x = x, y = y, group = line)) +
  geom_path(linewidth = 5,
            show.legend = FALSE,
            colour = cols_gpcds$graph_tertiary_lighter) +
    geom_segment(data = data_arrows_left_and_right,
               aes(x = xmin, y = ymax, xend = xmax, yend = ymin, group = line),
               arrow = arrow(type="closed", ends = "last"), linewidth = 10, show.legend = FALSE,
               colour = cols_gpcds$story_tertiary_lighter)

Combining this altogether and making it prettier again:

gg_left_to_right <- data_left_and_right %>%
  ggplot(aes(x = x, y = y, group = line)) +
    geom_segment(data = data_arrows_left_and_right,
               aes(x = xmin, y = ymax, xend = xmax, yend = ymin, group = line),
               arrow = arrow(type="closed", ends = "last"), linewidth = 5, show.legend = FALSE) + 
  geom_path(linewidth = 5,
            show.legend = FALSE,
            aes(colour = ifelse(between(line, 1, 6), "main", "background"))) +
  scale_x_continuous(expand = expansion(0, -0.1)) +
  scale_y_continuous(expand = expansion(0, 0)) +
  scale_colour_manual(values = c("main" = "black",
                                 "background" = "grey80")) +
  coord_fixed(ratio = 1 / 2, ylim = c(0, 7), xlim = c(0, 2*pi)) +
  theme_void() +
  theme(
    panel.background = element_rect(fill = "#9A7D66", colour = "transparent"),
    panel.border = element_blank()
  ) 

gg_right_to_left <- data_left_and_right %>%
  ggplot(aes(x = x, y = y, group = line)) +
    geom_segment(data = data_arrows_left_and_right,
               aes(x = xmin, y = ymax, xend = xmax, yend = ymin, group = line),
               arrow = arrow(type="closed", ends = "first"), linewidth = 5, show.legend = FALSE) + 
  geom_path(linewidth = 5,
            show.legend = FALSE,
            aes(colour = ifelse(between(line, 1, 6), "main", "background"))) +
  scale_x_continuous(expand = expansion(0, -0.1)) +
  scale_y_continuous(expand = expansion(0, 0)) +
  scale_colour_manual(values = c("main" = "black",
                                 "background" = "grey80")) +
  coord_fixed(ratio = 1 / 2, ylim = c(0, 7), xlim = c(0, 2*pi)) +
  theme_void() +
  theme(
    panel.background = element_rect(fill = "#9A7D66", colour = "transparent"),
    panel.border = element_blank()
  ) 

ggptch_left_and_right <- gg_left_to_right + theme(plot.margin = margin(r = 20)) | gg_right_to_left

ggptch_left_and_right %>% 
  ggsave(quarto_here("ggptch_left_and_right.png"),
         .,
         width = 5 * 2 + 0.5,
         height = 2.5 * 2 + 1.5)

Cool! I like those. Now let’s make the vertical versions by swapping the x and y coordinates and combine them altogether with {patchwork}

seq_x_tb <- seq(from = -0.5,
                  to = 2.5 * pi, 
                  by = pi / 100)
n_lines <- 11

data_top_and_bottom <- tibble(x = rep(seq_x_tb, 9),
       line = rep(seq(-1, 7), each = length(seq_x_tb))) %>% 
  mutate(y = line + sin(x)) 

data_arrows_bottom_and_top <- data_top_and_bottom %>% 
  filter(x %in% c(seq_x_tb[c(length(seq_x_tb) / 2 -1 , length(seq_x_tb) / 2 + 1)]),
         between(line, 1, 6)) %>% 
  group_by(line) %>%
  summarise(xmin = min(x),
        xmax = max(x),
        ymax = max(y),
        ymin = min(y))

gg_top_to_bottom <- data_top_and_bottom %>%
  ggplot(aes(y = x, x = y, group = line)) +
    geom_segment(data = data_arrows_bottom_and_top,
               aes(y = xmin, x = ymax, yend = xmax, xend = ymin, group = line),
               arrow = arrow(type="closed", ends = "first"), linewidth = 5, show.legend = FALSE) +
  geom_path(linewidth = 5,
            show.legend = FALSE,
            aes(colour = ifelse(between(line, 1, 6), "main", "background"))) +
  scale_x_continuous(expand = expansion(0, -0.1)) +
  scale_y_continuous(expand = expansion(0, 0)) +
  scale_colour_manual(values = c("main" = "black",
                                 "background" = "grey80")) +
  coord_fixed(ratio = 1 / 2, ylim = c(0, 7), xlim = c(0, 2 * pi)) +
  theme_void() +
  theme(
    panel.background = element_rect(fill = "#9A7D66", colour = "transparent"),
    panel.border = element_blank()
  ) 

gg_bottom_to_top <- data_top_and_bottom %>%
  ggplot(aes(y = x, x = y, group = line)) +
    geom_segment(data = data_arrows_bottom_and_top,
               aes(y = xmin, x = ymax, yend = xmax, xend = ymin, group = line),
               arrow = arrow(type="closed", ends = "last"), linewidth = 5, show.legend = FALSE) +
  geom_path(linewidth = 5,
            show.legend = FALSE,
            aes(colour = ifelse(between(line, 1, 6), "main", "background"))) +
  scale_x_continuous(expand = expansion(0, -0.1)) +
  scale_y_continuous(expand = expansion(0, 0)) +
  scale_colour_manual(values = c("main" = "black",
                                 "background" = "grey80")) +
  coord_fixed(ratio = 1 / 2, ylim = c(0, 7), xlim = c(0, 2 * pi)) +
  theme_void() +
  theme(
    panel.background = element_rect(fill = "#9A7D66", colour = "transparent"),
    panel.border = element_blank()
  ) 


(gg_top_to_bottom + theme(plot.margin = margin(r = 20)) | gg_bottom_to_top)

ggptch_all_directions <- (gg_left_to_right + theme(plot.margin = margin(r = 20)) | gg_right_to_left) / 
(gg_top_to_bottom + theme(plot.margin = margin(r = 20)) | gg_bottom_to_top)

ggptch_all_directions %>% 
  ggsave(quarto_here("ggptch_all_directions.png"),
         .,
         width = 5 * 2 + 0.5,
         height = 2.5 * 2 + 1.5)

In an ideal world I’d play around with the vertical images to make them align better, but I can’t quite figure out how to do that today. Hopefully you’ll be seeing these charts again in a project soon. But even if not, I’m quite happy with how they look 😀