Ripple Effects: Wave Algorithm

December 20, 2006

Flynn-Burhoe, Maureen. 2006. Ripples Algorithm
Applying algorithms to ripples is as necessary in art as in science. Those applied by artists are invisible and unconscious but omnipresent. I googled for measurements to better understand M. C. Escher’s linogravure (1950) Cercles dans eau in relation to Andrew Davidhazy‘s photographs of the ripple effect of a drop disturbing the calm surface of a body of water.

I wanted to compare the measurements for the angles at which both these images were captured. I had layered them but they were not the same at all. This image was viewed on my Flickr account 2,843 times from October 22, 2006 when I first uploaded it to January 29, 2007. I finally printed it out in December 2006 at Apple Printers in Duncan, BC. The print quality potential at the shop is excellent but the image did not stand up to a printout! The layer of Escher’s print is too bluntly cut off and I was disappointed in the edges of my globes. So I opened all my original files again and went to work to clean it up. I realized that the angles at which Escher and Davidhazy captured their images, were different.

Andrew Davidhazy’s photographs of water splashes

“concentrate on the after effects of the impact of a drop of water on a shallow layer of the same liquid. He documents an aspect of fluid mechanics. This is a recoil or rebound effect of the surface responding to the sudden disturbance caused by a drop of water hitting the surface. The recoil column of water rises to surprising elevations above the surface and then due to surface tension effects it breaks up into droplets that fall back into the host liquid under the pull of gravity.”

Of course, I knew Escher’s original print was a double-ripple on a mirrored surface clearly reflecting branches of a tree without any leaves against a white sun. The serenity of Davidhazy’s photo could not be interrupted with an entire tree! But I would have liked to have had a better resonance between the angles of the ripples. There was more than one question. How do you measure the angle of perspective of the ripples? How do you measure a ripple affect? The first is basic Renaissance perspective but the second . . .

When professor Mikhail Nesterenko describes wave algorithms his descriptions are written in the language of computers and science: mathematics, engineering and physics but there is something of the philosophical that engaged me . . . almost poetry.

In this <a href=”http://www.photoblog.com/user/oceanflynn/2006/12/19″>image on my photoblog</a> I layered a sections of his description with a detail of M. C. Escher’s print. So which kind of algorithm is used by Escher and Davidhazy?

“Wave algorithm satisfies the following three properties:

  1. Termination: each computation is finite
  2. Decision: each computation contains at least one decide event
  3. Dependence: in each computation each decide event is causally preceded by an event in each process
  • initiator(starter) – process that execution of its actions spontaneously
  • non-initiator(follower) – starts execution only when receives a message

Wave algorithms differ in many respects, some features:

  • Centralized (single-source)
  • – one initiator; decentralized (multisource)
  • – multiple initiators

Topology – ring, tree, clique, etc.
Initial knowledge:

  • Each process knows its own unique name
  • Each process knows the names of its neighbors
  • Number of decisions to occur in each process
  • Usually wave algorithms exchange messages with no content


Andrew Davidhazy also works with digital strip panaroma of 360 degrees views

For more on stunning visual effects of fluid mechanics see Alex Liberzon’s site here. . he is a Senior Lecturer at the Department of Fluid Mechanics and Heat Transfer, Faculty of Engineering of the Tel Aviv University.

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