I was playing around with the Riemann zeta function from the `pracma`

package – trying to find the best way to visualise it and specifically, its zeros. The zeta function, of course, is given by:

All non-trivial values of exist for with . The way I choose to visualise it was the polar plot of for values and .

library(pracma) library(ggplot2) library(gganimate) library(dplyr) #### Create complex set vector #### # Imaginary parts y <- seq(0, 100, len = 10001) # Complex vector z <- 0.5 + y * 1i #### Evaluation of Zeta function #### # Real part real_ <- Re(zeta(z)) # Imaginary part imaginary <- Im(zeta(z)) #### Plotting #### zeta_df <- data.frame(real_ = real_, imag = imaginary, frame_ = 1:10001) g <- zeta_df %>% ggplot(aes(x = real_, y = imaginary, frame = frame_)) + geom_path(size = 1.2, aes(cumulative = T)) + geom_point(size = 2, aes(x = 0, y = 0)) gganimate(p = g, filename = "riemann.mp4", interval = 0.001, title_frame = F) } |