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A periodic shift in Polar Roses for Valentines Day
|| 2/14/2007 || 6:28 am || Comments Off || ||

Original Process:
grantpark rectangle6 A periodic shift in Polar Roses for Valentines Day
Shifted to the right (or left)
grantpark rectangle shift6 A periodic shift in Polar Roses for Valentines Day
Zoom of Grant Park Quilt

Last month I thoroughly explored the applications of geometric tessellations using the polar coordinate filter. After doing a bit more research I discovered how similar these “amazing circles” appear to be very similar to the sinusoidal curves of a Polar Rose. They use the equation:

cos A periodic shift in Polar Roses for Valentines Day

In the original process I used to construct last month’s Polar Roses each interation added one tile to the entire panorama. I believe this represents the a in the equation. And after each iteration, there would be a new pedal added.

Today’s discovery is the realization of how these panoramas are wrapped around a cylinder to produce the pedals when the polar coordinate system is used. I’ve been working in whole numbers only, yet if the tiles are wrapped in a cylindrically fashion using a half shift, there will be a change in the pedal’s layout.

So to create this shift, half of one tile is removed on each end (notice above), and when they connect after being wrapped around a cylinder they still form a perfect tessellation and thus new pedal configuration when the filter is applied.

The result of this polar shift is quite interesting- a 90 degree rotation for each iteration.

View the 90 degree difference:
Old:

grantpark polar6 A periodic shift in Polar Roses for Valentines Day

Shifted 90 degrees:

grantpark polar shift6 A periodic shift in Polar Roses for Valentines Day

I can now apply this periodic shift to each of the geometries to produce a completely new set of Polar Roses. This should be interesting.



Post Title: A periodic shift in Polar Roses for Valentines Day
Posted in: Grant Park, Hexagon, Illinois, Location, Polar Coordinates, Quilt, Renderings
Last edited by Nikolas Schiller on 7/29/2009 at 8:48 pm



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Nikolas Schiller is a second-class American citizen living in America's last colony, Washington, DC. This blog is my on-line repository of what I have created or found on-line since May of 2004. If you have any questions or comments, please contact:

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