; Date: Mon, 27 Sep 2004 11:53:59 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 27-09-04 (Seahorse Scene [4]) ; Id: <1.5.4.16.20040927115448.0d5f845c@pop.mindspring.com> ; --------- ; ; FOTD -- September 27, 2004 (Rating 4) ; ; Fractal visionaries and enthusiasts: ; ; Today's fractal gives us a new view of a midget lying in the ; Seahorse Valley area of the Mandelbrot set. This valley, which ; separates the main bay from the largest bud, is perhaps the ; best-known feature of the Set. When its aspect in the M-set ; alone is considered, Seahorse Valley appears as two two-dimen- ; sional wedges that approach but never quite reach the X-axis. ; But the Mandelbrot set is but a single slice of a monstrous, ; four-dimensional abstraction known as the Julibrot, and Seahorse ; Valley itself is but a single slice of a much broader four-dimen- ; sional part of the Julibrot. ; ; Being a 4-D object, the totality of Seahorse Valley cannot be ; visualized, but it can be discussed. In the M-set, the valley ; terminates in two sharp points. The M-set lacks two dimensions ; of the Julibrot however. When one dimension is added, the ; valley may be visualized as terminating in two sharp edges that ; approach each other but never quite touch. This much can be ; easily visualized. But when still another dimension is added, ; the valley must be seen as terminating in two sharp surfaces, ; which could extend indefinitely in the plane of their two dimen- ; sions and still be as sharp as a razor at every point. ; ; The idea makes no sense. A flat surface is a two-dimensional ; wall that cannot be sharp. This is true enough in three-dimen- ; sional space, but in four-dimensional space, a 2-D surface with ; no extent in the remaining two dimensions is a razor edge that ; could slice cleanly through any soft 4-D object it touches. ; ; These words are easy enough to understand, but like so many ; other features of 4-D space, the thing they describe cannot be ; visualized. Curiously enough, a properly programmed computer ; would have no trouble moving and turning 4-D objects in 4-D ; space, but even when it did so, we would see only morphing and ; turning 3-D shapes on our flat 2-D screens. Is the inability to ; visualize four-dimensional objects a limitation of our 3-D ; visual apparatus, is it a limitation of our minds, or are we ; merely unable to imagine an abstraction that does not physically ; exist? ; ; Regardless, today's image is easily viewable. I named it ; "Seahorse Scene" because, even though it is sliced at an unimag- ; inable angle, the scene is still located in Seahorse Valley. I ; rated it at a 4 because I can see little in it that is worth ; more. When the render time of 10-1/4 minutes is considered, the ; overall value equals 39. All this rating stuff can be avoided ; by visiting the FOTD web site and downloading the finished image ; from there. The FOTD web site may be accessed at: ; ; ; ; Continuing near perfect weather here at Fractal Central on both ; Saturday and Sunday kept the fractal cats quite happy. They ; spent the better part of both days lounging in the yard, ; sleeping and remembering the days when they still had their ; kittenish enthusiasm. Today is starting acceptably well. ; Tomorrow promises rain, so the duo had best enjoy themselves as ; much as possible today. ; ; For me, things are nearly caught up. Unless something ; unexpected happens, I should be able to return the FOTD to its ; one-a-day schedule on October 1. And I might even have time ; for some deep philosophical discussion. The next FOTD fractal ; will appear on Sep 29. Until then, take care, and search for ; the entrance to the fourth dimension. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE================================ Seahorse_Scene { ; time=0:10:14.17--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=+0.00000000000102891/+0.000000000000197\ 56/6.53521e+011/0.02319/-9.79555128726789448/-85.9\ 814495713471274 params=42/147/2/0/-0.7475607140431\ 548/0.1243880653191712/-0.7475607140431548/0.12438\ 80653191712 float=y maxiter=4200 inside=0 logmap=1146 periodicity=10 colors=000qeYqfXrgWrhVsiUtjUsiTshSrgRrgQqfPqeOpeNp\ dMocLocKnbJnaImaHm`Gl_Fl_EkZDkYCjYBjXAiW9iW8hV7hU6\ gU5gT4fS3fS2eR1eQ0eQ0fP4fO8fNCgMGgLKgKOhJShIWhH_iG\ ciFgiEkjDojCskAzjCwjEujGsjIqjKojLmjNkjPijRgiTeiVci\ WaiY_i_YiaVicTieRifPihNhjLhlJhnHhpFhqDhsBhu9hw7hy5\ hz3ix4iv4iu4is4jr4jp4jo4jm4kl4kj4ki4kg4le5ld5lb5la\ 5m_5mZ5mX5mW5nU5nT5nR5nQ5mP6lP7kP7jP8iP9iP9hPAgPBf\ PBePCePCdPDcPEbPEaPF`PG`PG_PHZPIYPIXPJXPJVOKUNLSML\ RLMPKNOJNMIOLHOJGPIFQGEQFDRDCSCBSAAT9ATADRAFQAHOBK\ NBMLBOKCRICTHCVFCXED_DDaBDcAEf8Eh7Ej5Fm4Fo2Fq1Fs0D\ l5BeAAZF8SK6LP5EU37Z21c96WFAPLFHRJAVO2XN3YM3ZL3_K4\ aJ4bI4cH5dG5eF5gE6hD6iC6jB7kA7m97n88o78p68q58p8BoB\ DnEFmHHlJJkMLjPNiSPhURgXUf_WebYde_cgabjcame`pg`ri_\ jk_cmZXnZQpUHsZJqcKphLomMnqNmpMloMlnLknLkmKjlKjlKi\ kJijJhiIhiIhhHggHggHffGfeGedFedFdcFdbEcbEcaDc`Db_C\ b_CaZCaYB`YB`XA_WA_b1dWA_ } 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 PARAMETER FILE================================== ; ;