FOTD -- May 13, 2011 (Rating 7) Fractal visionaries and enthusiasts: Today's image shows the curious rectangle in its Parabolic aspect. Well, it's not exactly the Parabolic view, since the slice is rotated 30 degrees toward the Julia orientation. It might be difficult to pick out the rectangle at first glance. Actually, the rectangle is located at the top of the central pyramid, where it butts against the ceiling. A good part of the image, including the pyramids, consists of 'inside' stuff made visible by the 'bof61' inside fill. The 'outside' stuff fills the top part of the frame. I named the image "On-Stage Pyramids" when I had the impression of a theater stage filled with living pyramids performing their routine. But performing pyramids can be a rather dull act to watch, so I could rate the image no higher than a 7, which BTW is FOTD average. The calculation time of 2-1/2 minutes may be avoided by viewing the completed image on the FOTD web site at: <http://www.crosscanpuzzles.com/Archives.html> The high-fefinition version is posted at: <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> And the original FOTD web site may be accessed at: <http://www.Nahee.com/FOTD/> If I had three wishes, and it was forbidden to wish for extra wishes, the first wish would be to gain the ability to visualize the fourth spatial dimension without resorting to the trick of using time as the fourth dimension. I know all the parts of simple 4-D objects such as the hypercube and hypersphere, but even after all these years I am unable to connect the parts into a single hyper-object. Then I wonder how a person would react if they suddenly found themselves with a 4-D body living in a 4-D world. If they could survive the sensory overload, would they recognize the things they previously could picture only one 3-D section at a time? Would they recognize a hypercube or hypersphere, and what about that strange 4-D object with no analog in 3-D space, the 24-cell? How would they cope with the experience of walking on a planet where the horizon appears as a sphere surrounding them in all directions, even the directions we in 3-D space call up and down? Oh well, I guess it's a nice dream. Too bad I'll never be able to fulfill it. It's all very frustrating, so to whom do I complain about this inability to visualize the higher spaces that physicists are now claiming actually exist? Spring was in full swing here at Fractal Central on Thursday, as the temperature reached 79F 26C under bright sun. The fractal cats spent the day chasing the sun around the kitchen floor. The humans had one more in a long series of typical days, which seem to pass with nothing worth telling taking place. It should hardly be necessary to tell that the next FOTD will be posted in 24 hours. Until then, take care, and seek the answer where you least expect to find it. Jim Muth jamth@mindspring.com START PARAMETER FILE======================================= On-Stage_Pyramids { ; time=0:02:37.36-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 periodicity=6 center-mag=0/0.00603022/67.66976/0.1261/180 params=-30/90/90/0/-1.7435/0/0.00019/0.07388/2.003\ /0 float=y maxiter=750 inside=bof61 logmap=yes colors=0008FF9EG9EH99NADKADLACMBCNBBOBBPCARCASD9TD\ 9UD8VD5YE7YE7ZF6_F8`DA`FC_HEYIGZKIYLKWNMVPOUQQSSSR\ TTPVUEWWDYYB__A`a8bc7ce5eg4gi3ik1kl0mm0on0qo0sp0uq\ 0wt0zw0zz0zw0zu0zs0zq0zo0zm0zk0zi0zg0ze0yc0xa0w_0v\ Y0uW0tU0sS0rQ0rO0rM0rK0sJ0sI0sH0sF0sE0tD0tC0tB0tA0\ t90t80u70u70u70u70u70u70u70u70u70u70u70u70u70u70u6\ 0u60u60u60u60u60u60u60u60u60v60v60v60v60v50v50v50v\ 50v50v50v50v50v50v50v50v50v50v50v50v40v40v40v40v40\ w40w40w40w40w40w40w40w40w40w40w40w40w40w40w40w40w4\ 0w40w40w40w40w40w40w40t40r50o60m70k80Kb6Kb6Ka6Ka6K\ a6Ka6K`6K`6K`6K_6K_6K_6K_6LZ6LZ6LZ6LY6LY6LY6LX6LX6\ LX6LX6LW6LW6MW6MV6MV6MV6MV6MU6MU6MU6MT6MT6MT6MT6MS\ 6NS6NS6NR6NR6NR6NR6NQ6NQ6NQ6NP6NUUNUUNUUOUUOUUOUUO\ UUOUUOUUOUUOUUOUUOUUOUUOUUPUUPUUPUUPUUPUUPUUPUUPUU\ PUUPUUPUUPUUPUUQUUQUUQUUQUUQUUQUUQUUQUUQUUQUUQUUQU\ UQUURUURUURUURUURUUWC6WB6 } frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc } END PARAMETER FILE=========================================