; Date: Wed, 11 May 2011 23:06:46 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 12-05-11 (It Has No Symmetry [8]) ; Id: <1.5.4.16.20110511230645.11e793ae@pop.earthlink.net> ; --------- ; ; FOTD -- May 12, 2011 (Rating 8) ; ; Fractal visionaries and enthusiasts: ; ; Today's image is a view of the curious Julia rectangle as it ; appears in the Oblate plane, which is determined by the real(Z) ; and imag(C) axes. When viewed from this angle and given an ; appropriate amount of stretching and skewing, the rectangle ; pretty much retains its rectangular shape. ; ; The name "It Has No Symmetry" accurately describes the image. ; At first glance, the image does indeed appear to have origin ; symmetry, but a close inspection will reveal small discrepancies. ; ; The rating of an 8 could have been a half point or so higher if ; I had not re-used a previous color palette. ; ; The calculation time of 3 minutes is well within reason, but all ; the fuss and bother that goes with setting up and calculating ; a parameter file may be forgotten by viewing the finished image ; on the FOTD web site at: ; ; ; ; The image may be seen in hi-def at: ; ; ; ; Paul's original FOTD web site may be accessed at: ; ; ; ; I find the inability of the human mind to visualize the fourth ; dimension most curious. Computers have no problem converting ; the math of the fourth dimension to spatial coordinates and ; manipulating the resulting spatial figures exactly as they do ; with everyday 3-D figures. It would even be possible to ; construct a monitor with a 3-D viewing surface, ready to be ; enjoyed by a 4-D viewer. Unfortunately, a normal 3-D man with ; his 2-D retinas would be able to view such a screen only from ; the 'edge-on' direction and would be unable to enjoy the 4-D ; show any more than he could enjoy viewing a normal flat screen ; edge on. ; ; Why are we limited to visualizing three dimensions, when such ; fascinating things as double rotation and undistorted Klein ; bottles exist only one dimension higher. It is impossible for ; us to imagine even a 2-D flatland or a 1-D line without automati- ; cally mentally embedding these lesser spaces in a surrounding ; 3-D space. The limitation is not due to the math, which merely ; grows more tedious as the number of dimensions increases, with ; nothing of a totally new nature appearing. ; ; There is a theory, not entirely scientific, that our inability ; to visualize 4-D figures is a limitation of our level of con- ; sciousness, which is stuck at the 3-D level. This would imply ; that a being with a higher level of consciousness might be able ; to visualize the fourth dimension, or might even interpret the ; sensory impressions of the world he lives in as possessing four ; spatial dimensions. If so, he would not be around too long to ; enjoy his advantage. Stable planetary orbits are impossible in ; a space of four dimensions with its inverse-cube law, and if our ; math is correct, a planet in 4-D space would either spiral into ; its star or spin off into interstellar space. ; ; But then again, maybe a 4-D man would have different laws. ; ; The days keep getting better here at Fractal Central. Wednesday ; featured cloudless skies, gentle breezes and a cat-pleasing ; temperature of 77F 25C. The fractal cats, totally pleased, ; spent the day sleeping and dreaming of what they might do if ; they ever get to go outside. ; ; The humans had more mundane things to attend to. The next FOTD ; will be posted in 24 hours. It will likely be another view of ; the rectangle. There is still much yet to be discovered in the ; vicinity. Until then, take care, and Nostradamus says the world ; will end in 589 days. It's got ME worried. I thought we had ; 5-1/2 billion years. ; ; ; Jim Muth ; jamth@mindspring.com ; ; ; START PARAMETER FILE======================================= It_Has_No_Symmetry { ; time=0:03:04.77-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 center-mag=0/0\ /1130/0.02072/0/77 params=0/90/90/90/-1.7435/0/\ 0.00019/0.07388/2.003/0 float=y maxiter=15000 inside=0 logmap=62 symmetry=none periodicity=6 colors=000FDHFDJFELFCNFCPFCRGCSIETKGUMIXOK_QLbSNeU\ OhWQkYSm_ToaUqcTseSugRuiRukQvmPvoOvqOvpStrWst_rvcq\ xhpzmozrpzvszzvzzzzzzzzzzzzzzvzzrzzmzzgzzdzyazxazw\ azw`zv`zu`zt_zt_zs_zr_zqZzqZzpZzoYznYznYzmYzlXzkXz\ kXzjWziWzhWzhWzcSzZOzUKzPGvKCrF8mB5hC8cDBZEEUFHPGK\ OGMRHPUISXJV_KYaK_dLbgMejNhmOkoOmmRkkTjiVhgXgfZed`\ dbbb`daZf_YhZgh_ph_dcTTZMHUF5P99SEDUJHXOLZTO`XN_YN\ ZYNYYNYYNXYNWZNWZNVZNUZNUZNTZMS_MS_MR_MQ_MQ_Q9mQ9m\ P9cP9cO9cOAcNAcNAcMAcMAcLAcLAmKAmKAcJAcJAcIBcIBcHB\ cHBcGBcGCcFDcFEcEFcEGcDHcDIcCJcCKcBKcAKmAKmAKm9Kz9\ Kz8Kz8Kz7Kz7Kz6Kz6D65D65D54D54D53D53D42D42D42D47U8\ CiCHyGGzFGzFGzFGzFGzFGzFFzFFzFFzEFzEFzEFzEFzEEzEEz\ EEzEEzDczDczDczDczDczDczDczDczCzzCzzCzzCzzCzzCzzCz\ zCzzBzzBzzBzzBzzBzzBzzBzzBzzBzzmzzmzzmzzmzzmzzmzzm\ zzmzzmzzmzzmzzmzzmzzmzzmzzmzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz } 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 ;