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I can't find any reference in either of these images that you refer to with params=88/88/
Oops. Apparently I failed to make it clear that I was referring to modifying the parm 'file' contained *within that email*... Sorry to have you go to the trouble of looking for it in the wrong places. Oh! Also note that there was also an error in the date that Jim quoted as the original date the fractal enclosed in that email was posted. I duplicated that error in my previous email. The fractal was actually posted Jan 6th, 1998 rather than Jan 1st, 1998 that Jim erroneously said in his 7th Oct, 2003 FOTD post. I sent a follow-up email to [Philofractal] and [Fractint] revisiting this date issue. Just to be extremely clear, my previous email's subject was: Jim Muth's "...most surprising discovery of all [his] fractal explorations." Here's a snippet from that previous email showing the "params=88/88/" in question: ======= Quoted text =========== Until then, take care, and keep finding those fractal gems. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER-FORMULA FILE================= Projective_Plane { ; 3-1/2 min on a P200 at SF5 reset=1960 type=formula formulafile=multirot.frm formulaname=multi20031 function=flip/ident/ident\ /flip passes=1 center-mag=-0.00037327503160875/\ +0.00003799627771399/514.8005/1/25 params=88/88/0.00022/0.0755/-1.74308/0 float=y ==== End of Quoted text ============ I hope you're still willing to try those changes to the parameters. The results show a little of what can happen as things are rotated in small increments in the 4th dimension. Fortunately the fractals calculate relatively rapidly. Changing the parameters from 90/90 to 88/88 and then to 86/86 nicely reveal the trend of what happens to a geometric shape -- a rectangle -- as it gets warped in aesthetic ways. We don't often have the luxury of a geometric shape to start with to gauge its amount any type of distortion as a formula's parameters are varied, so I found this an opportunity I couldn't pass up. Actually, I should be using the evolver to look at many more of the possibilities in the Julibrot. It can effectively show four dimensions at once -- the two regular real and imaginary and whatever two additional parameters you choose to vary in the formula, say, rotations about two different multi-dimensional 'axes.' What a powerful way to explore! --------------------------------------------------- In Jim's FotD from September 19, 2006, named "Rectangle variation" he states that the fractal is derived from 'the original rectangle fractal.' That reference is what got me looking for the rectangle fractal that I remembered all these years. The thing that stuck with me was that a particular fractal (the tree-like pattern in the rectangle) formed by a simple substitution process (shown in Mandelbrot's book) could also be created by a complex iterated formula in a rotated slice from the four-dimensional Julibrot. I'm still amazed by that. In "Rectangle variation" you can still make out the 'rectangle' as the warped confetti-colored 'door mat' in the center of the action. The 'railroad switching yard' pattern prominent in Jim's September 17th, 2006 FotD is also visible in the periphery of "Rectangle variation." But the other material in "Rectangle variation" has apparently rotated into the image after being hidden in other dimensions... - Hal Lane ######################### # hallane@earthlink.net <mailto:hallane@earthlink.net> # #########################
-----Original Message----- From: Lee H. Skinner [mailto:skinner@thuntek.net] Sent: Tuesday, September 19, 2006 2:33 PM To: philofractal@lists.fractalus.com; Fractint and General Fractals Discussion Subject: Re: [philofractal] Jim Muth's "...most surprising discovery of all [his] fractal explorations."
Hal,
Jim's Sept. 17th FOTD: FractalOf_Tomorrow: params=45/45/...
Jim's Sept. 19th FOTD: RectangleVariation params=91.81/90.94/91.93/89.48/...
You say: ---------------------------------- If you remove both of Jim's two degree rotations by changing params=88/88/ to params=90/90/ the rectangle loses its slight curve and becomes very rectangle-like. However, the rectangle's tree-like pattern disappears and zooming cannot locate it.
If you increment both of Jim's two degree rotations by by two more degrees by changing params=88/88/ to params=86/86/ the rectangle becomes a comet complete with tail. The rectangle's/comet's tree-like pattern remains in this version. ------------------------------------------ I can't find any reference in either of these images that you refer to with params=88/88/
Am I missing something??
Lee ##############################################
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