Logarithmic Shell

This was my first creative coding experiment. It’s a simple connect-the-dots program that generates a spiral pattern resembling a shell. The visualization is based on the logarithmic spiral, a pattern that appears frequently in natural structures like shells, hurricanes, and galaxies.

Technical Implementation

The visualization is based on the logarithmic spiral. The equation for the logarithmic spiral is:

where $r$ is the distance from the origin, $\theta$ is the angle from the positive x-axis, $a$ is the starting radius, and $k$ is the growth factor. In this case, I used $a = 1$ and $k = 1/\pi$.

n <- 20
t <- seq(-pi, pi, length=n)
r <- exp(t/pi)
x <- r*cos(t)
y <- r*sin(t)

plot(x, y, type='n', asp=1) 
for (i in 1:n) for (j in 1:n) {
    xij <- x[c(i, j)]
    yij <- y[c(i, j)]
    lines(xij, yij, col='#F0F5')
}