; Date: Thu, 12 May 2011 17:50:18 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 13-05-11 (On-Stage Pyramids [7]) ; Id: <1.5.4.16.20110512175018.12c7a1d2@pop.earthlink.net> ; --------- ; ; 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: ; ; ; ; The high-fefinition version is posted at: ; ; ; ; And the original FOTD web site may be accessed at: ; ; ; ; 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========================================= ; ; ; ; _______________________________________________ ; Fractint mailing list ; Fractint@mailman.xmission.com ; http://mailman.xmission.com/cgi-bin/mailman/listinfo/fractint ;