Butterfly knn

butterfly_knn.R

# The curve is a generalisation of the butterfly curve (Fay, 1989)
# See the Wiki for details: https://en.wikipedia.org/wiki/Butterfly_curve_(transcendental)

# Load packages
library(mathart) # devtools::install_github("marcusvolz/mathart")
library(tidyverse)

# Set parameters
n <- 1000
a <- 2
b <- 7
c <- 8
d <- 17
e <- 7
f <- 1
g <- 5
h <- 2
i <- 17
j <- 9

# Generate data
df <- data.frame(t = seq(0, a*pi, b*pi/n)) %>%
  mutate(x = sin(t) * (exp(cos(t)) - c * cos(e*t) - (sin(t/i))^g),
         y = cos(t) * (exp(cos(t)) - d * cos(f*t) - (sin(t/j))^h)) %>%
  mutate(xend = lead(x), yend = lead(y)) %>%
  k_nearest_neighbour_graph(k = 100)

# Create plot
p <- ggplot() +
  geom_segment(aes(x, y, xend = xend, yend = yend), df, size = 0.03, alpha = 0.25) +
  coord_equal() +
  theme_blankcanvas(margin_cm = 0)

# Save plot
ggsave("butterfly_knn.png", width = 20, height = 20, units = "cm")