Phyllotaxis Sprial and Prime Numbers – Experiment

I recently tried out Data Camp’s project called “Phyllotaxis: Draw flowers using mathematics”. Now I’m hooked on drawing spirals using golden angle. Also the mathematical art on instructor’s blog, Fronkostin is just amazing!

Separately on twitter, I’ve gotten message on art with prime number, and that got me thinking to experiment with prime number & phyllotaxis flowers. I couldn’t figure out how I’d generate prime numbers in R, but I came across site where you can download prime numbers.

library(tidyverse)
library(patchwork)

## Read first 10000 digits of prime number!
prime <- read_csv(file="http://www.naturalnumbers.org/P-10000.txt", col_names=F)
names(prime) <- c("nth_prime","prime","int")  ## int = interval from previous prime number


## Function to Draw Frlower
my_flower <- function(points=5000,num_colour=9,col_option="magma",angle=pi*(3-sqrt(5)),...){
  flower <- tibble(
    n = c(1:points), ## change number here to use different # of points
    r = sqrt(n),
    is_prime = n %in% prime$prime, #logical
    colour = n%%num_colour, ## 2,3,6,12,18, seems to bring out the sprial pattern
    x = r * cos(angle*n),
    y = r * sin(angle*n)
  )
  
  prime.cnt <- flower %>% filter(is_prime) %>% count()
  angle_deg <- if(angle==pi*(3-sqrt(5))) {"golden angle!(137.51 degree | 2.4 radian)"} else {paste(round(angle*180/pi,2),"degree | ",round(angle,2),"radian")}
  
  ## Drawing Flower (but not using Prime Number)
  flower_plot <-flower %>%
    filter(!is_prime) %>%
    ggplot(aes(x=x, y=y, colour=colour)) +
    geom_point() +
    geom_path(size=0.01) +
    scale_colour_viridis_c(end=0.8, guide="none", option=col_option) +
    coord_fixed() +
    theme_void(base_family="Roboto Condensed") +
    labs(caption=paste(num_colour, "colours used to plot", points-prime.cnt,"dots.\nAngle Used: ", angle_deg), 
         subtitle="Flower Nibbled by Prime Number Bug")
  
  ## Drawing Flower (only using Prime Number)
  flower_prime <-flower %>%
    filter(is_prime) %>%
    ggplot(aes(x=x, y=y, colour=colour)) +
    geom_point() +
    scale_colour_viridis_c(end=0.8, guide="none", option=col_option) +
    coord_fixed() +
    theme_void(base_family="Roboto Condensed") +
    labs(caption=paste("Numbers between 1 and ",points, "have", prime.cnt," Prime Numbers\n"),
         subtitle="Flower made up by Prime Numbers Only")
  
  #You need to Print
  flower_plot + flower_prime
  
}

my_flower()  ## drawing with all default values e.g. 5000 points, 9 colours, angle= golden angle

my_flower(angle = 2*pi-(pi*(3-sqrt(5))))  ## changing angle 2pi - golden angle so it looks like it's the reverse of the above.

my_flower(angle=pi/sqrt(7))  ##  Just testing out different angles

my_flower(angle=pi/sqrt(pi), num_col=6*3) ## Using 18 different colours, but hard to distinguish the colour...  

my_flower(angle=exp(1), num_col=10) ## exp(1) = Euler's Number as angle. 

my_flower(angle = 0.3, num_col=3) ## All the black arm goes away when you only use prime number

my_flower(num_col=6*3, col_option="plasma") ## plasma colour palette! 

my_flower(points=10000,num_col=18, col_option="viridis")  ## little over crowded...