I have found a wonderful mardown by [Khac Phuoc Le][https://rpubs.com/iPhuoc/Phyllotaxis] where he explained how to use R to create imaginary flowers inspired by nature. He used ggplo2, which not surprising generated wonderful visualizations. I, however, wanted to follow his instructions but on basic R basic graphs. This is my result:

Drawing Points in a Circle

t <- seq(0, 2*pi, length.out = 50)
x <- sin(t)
y <- cos(t)

plot(x, y, pch= 19)

Making this Circle Armonious Using Golden Angle

# number of points
points <- 500

# golden angle

angle <- pi * (3 - sqrt(5))
  
t <- (1:points) * angle
x <- sin(t)
y <- cos(t)

plot(x*t, y*t, pch=19)

Removing Axes and Labs

plot(x*t, y*t, pch=19,
     xaxt="n", yaxt="n",
     bty= "n",
     xlab = "",
     ylab = "")

Size, Color, and Transparency

plot(x*t, y*t, pch=19, cex= 2.5,
     col = rgb(0,0.27,0.11,0.5),
     xaxt="n", yaxt="n",
     bty= "n",
     xlab = "",
     ylab = "")

Other Flowers

A Kind of Dandelion

plot(x*t, y*t, pch=8,cex=t/850,
     #col = rgb(0,0.27,0.11,0.5),
     xaxt="n", yaxt="n",
     bty= "n",
     xlab = "",
     ylab = "")

A Kind of Sunflower

par(bg="darkmagenta")
plot(x*t, y*t, pch=17,cex=t/350,
     col = rgb(1,1,0,0.5),
     xaxt="n", yaxt="n",
     bty= "n",
     xlab = "",
     ylab = "")

Changing angles

angle <- 2.0 
points <- 1000

t <- (1:points)*angle
x <- sin(t)
y <- cos(t)
par(bg="darkmagenta")
plot(x*t, y*t, pch=17,cex=t/750,
     col = rgb(1,1,0,0.5),
     xaxt="n", yaxt="n",
     bty= "n",
     xlab = "",
     ylab = "")

angle <- 13*pi/180 
points <- 2000

t <- (1:points)*angle
x <- sin(t)
y <- cos(t)
plot(x*t, y*t, pch=1,cex=t/90,
     col = rgb(0.57,0.57,0,0.1),
     xaxt="n", yaxt="n",
     bty= "n",
     xlab = "",
     ylab = "")

Further Experiments

angle <- 13*pi/180 
points <- 2000

t <- (1:points)*angle
x <- sin(t)
y <- cos(t)
plot(x*t, y*t, pch=1,cex=t/90,
     col = rgb(0.87,0.57,0,0.3),
     xaxt="n", yaxt="n",
     bty= "n",
     xlab = "",
     ylab = "")

# changing the size
plot(x*t, y*t, pch=1,cex=t/1000,
     col = rgb(0.87,0.57,0,0.3),
     xaxt="n", yaxt="n",
     bty= "n",
     xlab = "",
     ylab = "")

angle <- pi * (5/8- sqrt(5))

t <- (1:points) * angle
x <- sin(t)
y <- cos(t)
plot(x*t, y*t, pch= 19, col= rgb(0.9,1,0,0.5),
      xaxt="n", yaxt="n",
     bty= "n",
     xlab = "",
     ylab = "")

points <- 1000
angle <- exp(5/8- sqrt(5))

t <- (1:points) * angle
x <- sin(t)
y <- cos(t)
plot(x*t, y*t, pch= "!", col= rgb(0.6,0.8,0,0.4),
      xaxt="n", yaxt="n",
     bty= "n",
     xlab = "",
     ylab = "")

t <- 1:1000
f <- pi/100

plot(sqrt(t)* cos(t), sqrt(t)*sin(t), type ="l",
     lwd=2,
      col= rgb(0,1,0,0.4),
      xaxt="n", yaxt="n",
     bty= "n",
     xlab = "",
     ylab = "")

points <- 500

# golden angle

angle <- pi * (3 - sqrt(5))
  
t <- (1:points) * angle
x <- sin(t)
y <- cos(t)
plot(x*t, y*t, type="l", 
     col= rgb(0.6,0.8,0,0.4),
      xaxt="n", yaxt="n",
     bty= "n",
     xlab = "",
     ylab = "")

points <- 2000

# golden angle

angle <- pi * (3 - sqrt(5))
  
t <- (1:points) * angle
x <- sin(t)
y <- cos(t)
plot(x*t, y*t, type="l", 
     col= rgb(0.6,0.8,0,0.4),
      xaxt="n", yaxt="n",
     bty= "n",
     xlab = "",
     ylab = "")

points <- 1500

# angle

angle <-  exp(3 - sqrt(5))
  
t <- (1:points) * angle
x <- sin(t)
y <- cos(t)
plot(x*t, y*t, type="l", 
     col= rgb(0,1,0,0.7),
      xaxt="n", yaxt="n",
     bty= "n",
     xlab = "",
     ylab = "")

angle <- 167.4 * (3 - sqrt(5))

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


plot(x*t, y*t, type="l", 
     col= rgb(0.9,0,0,0.4),
     xaxt="n", yaxt="n",
     bty= "n",
     xlab = "",
     ylab = "")

points <- 1500

# golden angle

angle <- 137.3 * (3 - sqrt(5))

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


plot(x*t, y*t, pch= 19,
     col= rgb(0.9,0,0,0.4),
     xaxt="n", yaxt="n",
     bty= "n",
     xlab = "",
     ylab = "")

points <- 1500



angle <- 137.5 * (3 - sqrt(5))

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


plot(x*t, y*t, pch= 19,
     col= rgb(0.9,0,0,0.4),
     xaxt="n", yaxt="n",
     bty= "n",
     xlab = "",
     ylab = "")

points <- 1500

# golden angle

angle <- 137.6 * (3 - sqrt(5))

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


plot(x*t, y*t, pch= 19,
     col= rgb(0.9,0,0,0.4),
     xaxt="n", yaxt="n",
     bty= "n",
     xlab = "",
     ylab = "")