The set of affine maps that produced the graphics (which should, hopefully, spell out "HAPPY NEW YEAR!") are displayed below.  If it were possible to properly display the images, each word would be an infinitely nested version of itself.    (Which means, in part, that buried within HAPPY should lie infinite HAPPY-ness; and hiding within NEW should lie infinite NEW-ness.)   In the limit, each word would be a true fractal.   The images are actually approximations to the true fractals.  Both the approximations, and the true fractals, result from iterating the simple affine maps in the plane, R2, and are precisely given below. [And, if you wish, you can download (ridiculously, inefficiently large) .pdf files that display - approximately - infinite happy-ness, and infinite new-ness. Use the magnifying glass to zoom.]

                                        December 2004
                                        Rick Kreminski

Happy  =

{( 0.104718` + 0.0534926` x + 0.100647` y ), ( 0.0643674`ɯ ... 04; + 0.94845` x + 0.594562` y 0.729666` + 0.912454` x + 0.226005` y

New  =

{( 0.232947` + 0.165113` x + 0.120307` y ), ( 0.0936998`ɯ ... 62304; + 0.963819` x + 0.12582` y 0.90783` + 1.03351` x + 0.12582` y

Year  =

{( 0.29373` + 0.345074` x + 0.924816` y ), ( 0.0648985`ᡖ ... 04; + 0.802738` x + 0.171517` y 0.916441` + 0.965638` x + 0.343643` y

Created by Mathematica  (December 27, 2005)