The mirror image of the dahlia was created first and then the polar transformation was applied. Here is the written instructions:
Polar Coordinate Transformations
Photoshop CS5
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Open image in Photoshop
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Image needs to be an 8 bit image – to check if you don't know that it is 8 bit
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Image>Mode>8 bit/channel
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For square image – select Crop tool and set width and height dimensions the same
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Filter>Distort>Polar coordinates
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Select Polar to Rectangle and click OK
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Image>Image rotation>Flip canvas vertical
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Filter>Distort>Polar coordinates
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Select Rectangle to Polar and click OK
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Save results if satisfied or try another image
A square image will give a spherical look and a rectangular image will result in an elliptical look.
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