Mathematical art in R

Who says there's no art in mathematics? I've long admired the generative art that Thomas Lin Pedersen occasionally posts (and that you can see on Instagram), and though he's a prolific R user I'm not quite sure how he makes his art. Marcus Volz has another beautiful portfolio of generative art, and has also created an R package you can use to create your own designs: the mathart package. 

Generative art uses mathematical equations and standard graphical rendering tools (point and lines, color and transparency) to create designs. The mathart package provides a number of R functions to create some interesting designs from just a few equations. Complex designs emerge from just a few trigonometric functions, like this shell:

Or this abstract harmonograph:

Amazingly, the image above, and an infinite collection of images similar to it, is generated by just two equations implemented in R:

  x = A1*sin(t*f1+p1)*exp(-d1*t) + A2*sin(t*f2+p2)*exp(-d2*t),
  y = A3*sin(t*f3+p3)*exp(-d3*t) + A4*sin(t*f4+p4)*exp(-d4*t)

You can have a lot of fun playing around with the parameters to the harmonograph function to see what other interesting designs you can find. You can find that function, and functions for designs of birds, butterflies, hearts, and more in the mathart package available on Github and linked below.

Github (marcusvolz): mathart

Comments

[Michael Bedward]

Another great collection of mathematical art with R is Antonio Sánchez Chinchón's Fronkonstin blog.

[David Smith]

Thanks Michael, that's really cool!