Recursive Chessboard

For the mathematical background about this set, see this site (or this one). I first came across this transformation while browsing Seb Przd's photos. In a funny way, you can think of the inspiration been recursive too, since Seb in turn got it from lloydb.

All these images are transformed using the same formula (an exponentiation on the complex plane), but with different parameters. The parameters

Basically,

(1,0) with (2,0), you should see that the chessboard appears either once or twice at each level. Negative values (e.g., (-1,0)) flip the source image inside out, with the edges at the center and vice versa. It's also possible to use noninteger values for

There is no picture for

All these pictures were computed using the mathmap plug-in for The Gimp.

If you like this set, you may also be interested in my Recursion set. See also the Escher Droste group.

All these images are transformed using the same formula (an exponentiation on the complex plane), but with different parameters. The parameters

*(p1,p2)*used in the title of these pictures are the same as on the aforementioned site.Basically,

*p1*is the periodicity of the original picture. If you compare(1,0) with (2,0), you should see that the chessboard appears either once or twice at each level. Negative values (e.g., (-1,0)) flip the source image inside out, with the edges at the center and vice versa. It's also possible to use noninteger values for

*p1*, although this set does not demonstrate it (see for instance this picture with*p1=0.75*).*p2*controls the number of spirals: e.g., (1,-1) is a simple spiral, and (1,-2) is a double spiral. The sign of*p2*controls the direction of the spiral: the spiral grows clockwise if*p2*has the same sign as*p1*, otherwise it grows counterclockwise.There is no picture for

*(0,0)*, because that would filled by a single color.All these pictures were computed using the mathmap plug-in for The Gimp.

If you like this set, you may also be interested in my Recursion set. See also the Escher Droste group.

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