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Remember me, remember me, but ah! forget my fate (Dido’s Lament, Henry Purcell)

A Voronoi diagram divides a plane based on a set of original points. Each polygon, or Voronoi cell, contains an original point and all that are closer to that point than any other.

This is a nice example of a Voronoi tesselation. You can find good explanations of Voronoi diagrams and Delaunay triangulations here (in English) or here (in Spanish).

A grayscale image is simply a matrix where *darkness* of pixel located in coordinates (i, j) is represented by the value of its corresponding element of the matrix: a grayscale image is a dataset. This is a Voronoi diagraman of Frankenstein:

To do it I followed the next steps:

- Read this image
- Convert it to gray scale
- Turn it into a
*pure*black and white image - Obtain a random
*sample*of black pixels (previous image corresponds to a sample of 6.000 points) - Computes the Voronoi tesselation

Steps 1 to 3 were done with imager, a very appealing package to proccess and analice images. Step 5 was done with deldir, also a convenient package which computes Delaunay triangulation and the Dirichlet or Voronoi tessellations.

The next grid shows tesselations for sample size from 500 to 12.000 points and step equal to 500:

I gathered all previous images in this gif created with magick, another amazing package of R I discovered recently:

This is the code:

library(imager) library(dplyr) library(deldir) library(ggplot2) library(scales) # Download the image file="http://ereaderbackgrounds.com/movies/bw/Frankenstein.jpg" download.file(file, destfile = "frankenstein.jpg", mode = 'wb') # Read and convert to grayscale load.image("frankenstein.jpg") %>% grayscale() -> x # This is just to define frame limits x %>% as.data.frame() %>% group_by() %>% summarize(xmin=min(x), xmax=max(x), ymin=min(y), ymax=max(y)) %>% as.vector()->rw # Filter image to convert it to bw x %>% threshold("45%") %>% as.data.frame() -> df # Function to compute and plot Voronoi tesselation depending on sample size doPlot = function(n) { #Voronoi tesselation df %>% sample_n(n, weight=(1-value)) %>% select(x,y) %>% deldir(rw=rw, sort=TRUE) %>% .$dirsgs -> data # This is just to add some alpha to lines depending on its longitude data %>% mutate(long=sqrt((x1-x2)^2+(y1-y2)^2), alpha=findInterval(long, quantile(long, probs = seq(0, 1, length.out = 20)))/21)-> data # A little bit of ggplot to plot results data %>% ggplot(aes(alpha=(1-alpha))) + geom_segment(aes(x = x1, y = y1, xend = x2, yend = y2), color="black", lwd=1) + scale_x_continuous(expand=c(0,0))+ scale_y_continuous(expand=c(0,0), trans=reverse_trans())+ theme(legend.position = "none", panel.background = element_rect(fill="white"), axis.ticks = element_blank(), panel.grid = element_blank(), axis.title = element_blank(), axis.text = element_blank())->plot return(plot) } # I call the previous function and store resulting plot in jpeg format i=5000 name=paste0("frankie",i,".jpeg") jpeg(name, width = 600, height = 800, units = "px", quality = 100) doPlot(i) dev.off() # Once all images are stored I can create gif library(magick) frames=c() images=list.files(pattern="jpeg") for (i in length(images):1) { x=image_read(images[i]) x=image_scale(x, "300") c(x, frames) -> frames } animation=image_animate(frames, fps = 2) image_write(animation, "Frankenstein.gif")

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