Phyllotaxis

1. set-up library

# set-up library
library(ggplot2)

## Warning: package 'ggplot2' was built under R version 4.0.4

# set plot image
options(repr.plot.width = 4, repr.plot.height = 4)

2. Warmimg up: drawing point on a circle

# Create circle data plot
t <- seq(0, 2*pi, length.out = 50)
x <- sin(t)
y <- cos(t)
df <- data.frame(t, x, y)

# Make a scatter plot of points in a circle
p <- ggplot(data = df, aes(x, y))
p + geom_point()

3. Make it harmonious with the Golden Angle

# Define the number of points
points <- 500
# Define the Golden Angle
angle <- pi*(3-sqrt(5))

t <- (1:points) * angle
x <- sin(t)
y <-cos(t)
df <- data.frame(t, x, y)

# Make a scatter plot of points in a spiral
p <- ggplot(df, aes(x*t, y*t))
p + geom_point()

Remove everything unnecessary

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

# Make a scatter plot of points in a spiral and remove some plot components
p <- ggplot(df, aes(x*t, y*t))
p + geom_point() +
# .... YOUR CODE FOR TASK 4 ....
    theme(panel.background = element_rect(fill = "white"),
          axis.ticks = element_blank(),
          panel.grid = element_blank(),
          axis.title = element_blank(),
          axis.text = element_blank())   

#transpose angle
angle <- t(pi*(3-sqrt(5)))
df <- data.frame(t, x, y)

# Make a scatter plot of points in a spiral and remove some plot components
p <- ggplot(df, aes(x*t, y*t))
p + geom_point() +
# .... YOUR CODE FOR TASK 4 ....
    theme(panel.background = element_rect(fill = "white"),
          axis.ticks = element_blank(),
          panel.grid = element_blank(),
          axis.title = element_blank(),
          axis.text = element_blank())

5. A bit of makeup: size, color and transparency

# Change the code from Task 4 to modify the 
# size, transparency, and color of the points
p <- ggplot(df, aes(x*t, y*t))
p + geom_point(size = 8, alpha = 0.5, color = "#006400") + 
    theme(panel.background = element_rect(fill = "white"),
          panel.grid = element_blank(),
          line = element_blank(),
          title = element_blank(),
          text = element_blank())

6. Play with aesthetics: the dandelion

Until now, all points have the same appearance (size, color, shape, and alpha). Sometimes we will want to make the appearance of the points dependent on a variable in the dataset. Now we will make the size variable. We will also change the shape of the points. Although we won’t be able to blow on it, the resulting image should remind you of a dandelion.

p <- ggplot(df, aes(x*t, y*t))
p +  geom_point(aes(size = t), alpha = 0.5, shape = 8 ) + 
     theme(panel.background = element_rect(fill = "white"),
          panel.grid = element_blank(),
          line = element_blank(),
          title = element_blank(),
          text = element_blank(),
          legend.position = "none")

7. Put all it together: the sunflower

Plants not only use the Golden Angle to arrange leaves. The Golden Angle is also found in the arrangement of sunflower seeds. We don’t need anything new to draw a sunflower; we just need to combine some of the things we already know.

# Define the number of points
points <- 500
# Define the Golden Angle
angle <- pi*(3-sqrt(5))

t <- (1:points) * angle
x <- sin(t)
y <-cos(t)
df <- data.frame(t, x, y)


# shape of the points, and the background color
p <- ggplot(df, aes(x*t, y*t))
p + geom_point(aes(size = t), alpha = 0.5, shape = 17, color = "yellow") + 
    theme(panel.background = element_rect(fill = "darkmagenta"),
          panel.grid = element_blank(),
          line = element_blank(),
          title = element_blank(),
          text = element_blank(),
          legend.position = "none")

8. What if you modify the angle?

These patterns are very sensitive to the angle between the points that form the spiral. Small changes to the angle can generate very different images. Let’s look at an example of that.

# Change the value of the angle
angle <- 2.0
points <- 1000

t <- (1:points)*angle
x <- sin(t)
y <- cos(t)
df <- data.frame(t, x, y)

# Copy the plotting code from Task 7
p <- ggplot(df, aes(x*t, y*t))
p + geom_point(aes(size = t), alpha = 0.5, shape = 17, color = "yellow") + 
    theme(panel.background = element_rect(fill = "darkmagenta"),
          panel.grid = element_blank(),
          axis.ticks = element_blank(),
          axis.title = element_blank(),
          axis.text = element_blank(),
          legend.position = "none")

9. All together now: imaginary flowers

# Change the values of angle and points
angle <- 13*pi/180
points <- 2000

t <- (1:points)*angle
x <- sin(t)
y <- cos(t)
df <- data.frame(t, x, y)

# Adjust the plot parameters to create the magenta flower
p <- ggplot(df, aes(x*t, y*t))
p + geom_point(size = 80, alpha = 0.1, shape = 1, color = "magenta4")+
  theme(legend.position="none",
        panel.background = element_rect(fill = "white"),
        panel.grid=element_blank(),
        axis.ticks=element_blank(),
        axis.title=element_blank(),
        axis.text=element_blank())