Phyllotaxis

Harmonuos spiral shape

for a more harmonuos spiral shape we use the Golden Angle concept which is also related to the Golden Ratio

Golden Angle = π(3 − √5)

options(repr.plot.width = 5, repr.plot.height = 5)
library(ggplot2)
# Defining the number of points
points <- 500
# Defining the Golden Angle
angle <- pi * (3 - sqrt(5))

# remake the scatter plot again
# t <- seq(1*angle, 500*angle, length.out = 500) # t <- (1:points) * angle
t <- (1:points) * angle
x <- sin(t)
y <-cos(t)
df <- data.frame(t, x, y)
p <- ggplot(df, aes(x*t, y*t))
p + geom_point()

sun flower

p <- ggplot(df, aes(x*t, y*t))
p + geom_point(mapping = aes(size = t), alpha = 0.5, shape=17, color = "yellow") +
theme(panel.background = element_rect(fill = "white", colour = "darkmagenta"),
      title =  element_blank(), axis.ticks =  element_blank(),
      axis.text =  element_blank(), panel.grid =element_blank(),
      legend.position = "none")

Changing the angle effect

we change the golden angle, and we increase points number we set angle to 2 with 1000 points

    angle <- 2
    points <- 1000
    
    t <- (1:points)*angle
    x <- sin(t)
    y <- cos(t)
    
    df <- data.frame(t, x, y)
  
    p <- ggplot(df, aes(x*t, y*t))
    p + geom_point(mapping = aes(size = t), alpha = 0.5, shape=17, color = "yellow") +
    theme(panel.background = element_rect(fill = "white", colour = "darkmagenta"),
          title =  element_blank(), axis.ticks =  element_blank(),
          axis.text =  element_blank(), panel.grid =element_blank(),
          legend.position = "none")

ggsave("2.png", width = 4, height = 4)

Beautiful example

angle <- 13 * pi / 180
points <- 1300

t <- (1:points)*angle
x <- sin(t)
y <- cos(t)

df <- data.frame(t, x, y)

p <- ggplot(df, aes(x*t, y*t))
p + geom_point(size = 80, alpha = 0.1, shape=1, color = "magenta4") +
theme(panel.background = element_rect(fill = "white", colour = "darkmagenta"),
      title =  element_blank(), axis.ticks =  element_blank(),
      axis.text =  element_blank(), panel.grid =element_blank(),
      legend.position = "none")

ggsave("4.png", width = 3, height = 3)