FOTD -- January 12, 2002 (Rating 7) Fractal visionaries and enthusiasts: Today's image pictures a slice through the open area located at -1.99909595 on the negative stem of the Mandelbrot set. It also pictures a slice through the Julia sets of this hole, though the scene bears little resemblance to either a M-set or a J-set. because the image is a new aspect of an old thing, I have named it "A New Scene". The image in fact is what I call a Rectangular set. It is a slice through the same -1.99909595 hole, but instead of being sliced in the real(c),imag(c) direction, which gives Mandelbrot sets, or the real(z),imag(z) direction, which gives Julia sets, the hole has been sliced in the imag(c),imag(z) direction, which gives Rectangular sets. I named the fractals that result when the Julibrot is sliced in this direction "Rectangular" because as today's image shows, they are filled with holes that are shaped like rectangles. Today's image is quite different from either a Mandelbrot or Julia fractal, both of which are instantly recognized by fractal explorers, but like its better known cousins, it is also instantly recognizable, at least by myself, as a Rectangular fractal. Like Julia sets, which in the Z^2+C fractal are symmetrical around the origin, the Rectangular sets also display symmetry around the origin. But unlike Julia or Mandelbrot sets, the Rectangular sets are inherently distorted, and must be undistorted before they can be fully realized. In today's image, this undistorting takes the form of rotation, stretching and skewing. There are three more perpendicular directions in the Julibrot, in which this particular hole can be sliced at today's point. I will show these three additional aspects, which I have named Oblate, Parabolic and Elliptic, in the next three FOTD's. Because today's image takes a familiar old object and makes something totally new of it, I have given it a rating of 7. An extra benefit is the lightning speed of the parameter file, which renders in a matter of seconds. For those who cannot run the parameter file, the finished image may be available on Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> But Paul's site has not been updated recently. If the image is not yet on Paul's site, try Scott's FOTD site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The Friday weather here at Fractal Central started with a shower of rain, then cleared, but turned blustery and colder in the afternoon. The fractal cats don't like rain, they don't like wind, and they don't like cold. As a result, they were unhappy fractal cats until I opened the traditional can of tuna for them. (Sometimes I wonder if the cats just pretend to be unhappy to manipulate me into giving them tuna instead of cat food!) It's now time to do some week-end odd jobs that need to be done. Until next FOTD, take care, and be yourself. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ A_New_Scene { ; time=0:01:15.63--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=0/0/2.176732e+007/0.3076/-47.2379488575\ 538815/60.6611623140979432 params=90/90/2/0/-1.999\ 09595/0/-1.99909595/0 float=y maxiter=5000 inside=0 logmap=40 colors=000ZWoYWoXUnWTnVTmUTmTTlSTlRTkQTk\ PTjOTjNTiMSiLRhKQgJPfJOeINdIMcHLbHKaGJ`GI_FHZFGYEF\ XEEWDEVDCUCATF6QFDPAKQ4SP0ZO0dV0l`0rf0sc0s`0uY0uV0\ vS0vP0xM0xJ0yG0yD0zA0z70z40z3Cv0Yr0sl0zg0za0zX0zS0\ zM0zI3zJ4zL6zM7zO9zOAzPCzQDzSFyTGxTGsVLoVOjXQfXTaX\ YYY`TYcPYfL_jG_mC`p7`s3`x0az0az0az0Pz0Cz0Az09z07z0\ 6z04z13z31z41zdCVzL0zJ0yI0rG0jG4cF7XDCPDGICLAAP3AS\ 4IO6OL7VI9`DAgACm7Cs4Io7Ol9TiC_fDdcGj`IoYJjVLgSMcP\ O`MOYJPTGQQDQMASJ7TG4TC1V90X60XJ0OV0GL69Q39X09a090\ zA6j9IT9VC9z0Or0GzDzzAzz7ux6lu3dp0Xm0Pi0Gu9fr6`o3V\ m1Pj0Jg0DJD0P91T43Y16a07aOjcG`d9Sf1IxPmmjLjYIiLFg7\ CdYJfSIfOGfIFfDDf9CGYL0XF7c7Oi0co0su0um0vf0v_3xS7y\ LDyDIz6Oz0SuAVpJXlSYf`_ai`Yradsdlsgssjzvmzzpzzszzo\ uzjjzf`zaQzYGzVPz_Xzcczgjzjdzg_zfTzcOzaIz_CzYJzXPz\ XVzV`zVgzVmzTszTyzTzzYzzazzfzzjzzozzszzzzzzzzzzzzz\ zzzzzzzziziIzO0z1czVczMczDzz4zzGvzS } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================