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 (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 plugin for The Gimp.
If you like this set, you may also be interested in my Recursion set. See also the Escher Droste group.
30 photos  13,943 views
Comments on this set
Seb Przd says:Excellent set! 

dmswart says:Wonderful set here. 

Seb Przd says:Dans ton explication (très claire d'ailleurs! bravo), il faut corriger la partie sur p1 et l'exemple (0,1), (0,2). 

gadl says:Merci, c'est corrigé. J'en ai profité pour tenter d'expliquer les p1 négatifs. 

Sam Rohn  360° Photography says:these are both beautiful and informative, a great help in my getting my nonmathematically inclined brain around this droste biz.... 

alterednate says:I could only hope to achieve one day such an interesting way of looking at space using photographs  well done!! 

Nicolas Burtey says:Very didactic work. 

amuse says:Outstanding set In everyway! 

Mazapán [deleted] says:terrific, i love them, good work! 

Michael LaPalme says:Fantastic set. Thanks for posting the details also. Very interesting. 