Andrew Yeckel > Art Gallery > Mondrian Collection

Mondrian Collection

Everything shown here is Copyright © 2019 Andrew Yeckel, all rights reserved

The upper left image, my knockoff of Piet Mondrian's 1928 painting, Large Composition with Red, Blue, and Yellow, represents the initial distribution of colored particles in a box. The other images are generated by allowing this reference image to mix for varying lengths of time when the top and bottom walls are translated in opposite directions.

          

 

        

 

          

I've had the collection printed on 17 x 26 inch stretched canvases. For now they are stacked on this wall in my house, but I can imagine them strung out down a corridor in a hotel or commercial building:

These also look good in a float frame:

These images remain sharp at any enlargement. You need to see these canvases in person to fully appreciate them.

How these were made

These pictures were made by computing particle pathlines in a closed box. Stokes flow is driven by lateral motion of the top and bottom surfaces, which creates a vortex pair having two lobes enclosed by a streamline in the shape of a figure eight or hourglass, as shown below. Strictly speaking the U velocity is parabolic rather than constant along the top and bottom surfaces. I do this to avoid a discontinuity at the corners, which gives a smoother flow that is better suited to this type of visualization.

Particles are colored to match the painting wherever they are initially released into the flow. Particles that are released within the lobes will remain trapped there, and particles released outside the lobes will circulate around the outside. We can see that the upper lobe encloses mostly red with a little blue, and the lower lobe encloses nearly equal amounts of blue and yellow. These ratios are preserved throughout mixing.