Received: by mail.san.rr.com for ehill1 (with Cubic Circle's cucipop (v1.21 1997/08/10) Wed Jan 28 11:58:01 1998) X-From_: owner-fractal-art@aros.net Wed Jan 28 11:53 PST 1998 Received: from mars.aros.net (mars.aros.net [207.173.16.20]) by mail-atm.san.rr.com (8.8.7/8.8.8) with ESMTP id LAA11820 for ; Wed, 28 Jan 1998 11:53:38 -0800 (PST) Received: from terra.aros.net (terra.aros.net [207.173.16.10]) by mars.aros.net (8.8.7/8.8.4) with ESMTP id MAA26728; Wed, 28 Jan 1998 12:50:24 -0700 (MST) Received: (from majordom@localhost) by terra.aros.net (8.8.7/8.6.12) id MAA06055 for fractal-art-safe-outgoing; Wed, 28 Jan 1998 12:51:31 -0700 Received: from mars.aros.net (mars.aros.net [207.173.16.20]) by terra.aros.net (8.8.7/8.6.12) with ESMTP id MAA06051 for ; Wed, 28 Jan 1998 12:51:29 -0700 Received: from droid.nosc.mil (root@droid.nosc.mil [198.253.206.12]) by mars.aros.net (8.8.7/8.8.4) with ESMTP id MAA26616 for ; Wed, 28 Jan 1998 12:49:40 -0700 (MST) Received: from NOTESGW.NOSC.MIL (notesgw.nosc.mil [198.253.77.61]) by droid.nosc.mil (8.8.7/8.8.7) with SMTP id LAA28063 for ; Wed, 28 Jan 1998 11:47:32 -0800 (PST) Received: by NOTESGW.NOSC.MIL(Lotus SMTP MTA v1.1 (385.6 5-6-1997)) id 8825659A.006C7829 ; Wed, 28 Jan 1998 11:44:46 -0800 X-Authentication-Warning: terra.aros.net: majordom set sender to owner-fractal-art using -f X-Lotus-FromDomain: ACMS From: "Jay Hill" To: fractal-art@aros.net Message-ID: <8825659A.0067F1FB.00@NOTESGW.NOSC.MIL> Date: Wed, 28 Jan 1998 11:38:49 -0800 Subject: Re: F.O.T.D., 27-01 (String of Bays) Mime-Version: 1.0 Sender: owner-fractal-art@aros.net Precedence: bulk Reply-To: fractal-art@aros.net Content-Type: text/plain; charset=US-ASCII Content-Length: 2396 Jim Muth wrote: > I got the idea from Jay's panorama fractals, which draw a > panorama from the point of the M-set that corresponds to the > value assigned C. In such fractals, the farther from the > C-point an object lies, the smaller it appears. Then I > thought of the series of bays on the X-axis, which as they > grow smaller, converge in a regular sequence to a point near > -1.4 on the X-axis. (There is a name for this point, which > begins with L, but I can't recall it at the moment.) It is the Feigenbaum point, named for the man who discovered the constant ratio showing up in many non-linear processes. http://www.mathsoft.com/asolve/constant/fgnbaum/fgnbaum.html I have calculated this constant to about 50 digits. If you use more precision in the constant (the view point) you get more consistent bays. The value here should be good for another several bays. Also upping the iteration count to the max is a good idea. Using this picture, one can estimate the angle formed by the series of buds (bays) in the normal MSet (the vertical width). Also one can see the value of Feigenbaum's constant, 4.669... since its logarithm is the spacing of the bays. Jim, this is a great image. One can appreciate your Fractal of the Day series even more after trying to match you step for step for a few weeks! I sure hope Dr. J gets over his bowl fever real soon, I'm going to run out of ideas. :-) Enjoy Jay String_of_bays_J { ; par file, 16min at 100mhz, 640x480 ; from an idea by Jay Hill and Dr. J. ; original by Jim Muth, this one pushed to the limit by Jay Hill reset=1960 type=formula formulafile=test03.frm formulaname=test0622 function=exp center-mag=-8.17261/0/0.1936362/0.75 params=0/0/-1.4011551890920506/0 float=y maxiter=2147483647 ; bailout=16 inside=0 logmap=yes symmetry=xaxis periodicity=10 colors=000EEOGAK<30>2fq1hu<19>Be89h1<39>TMe\ POp<13>_JP`INaILaIKbJJcJJ<27>wUIzYB<37>hAur8x<7>IGp3Im<15>\ _HraHrbEu<33>dWadX`dYa<6>dW`EEPEEO savename=Fieg-bay } frm:Test0622 { ; Jim Muth z=p1, c=fn1(pixel)+p2: z=sqr(z)+c |z| <16 } ------------------------------------------------------------- Thanks for using Fractal-Art, The Fractal Art Discussion List Post Message: fractal-art@aros.net Get Commands: majordomo@aros.net "help" Administrator: noring@netcom.com Unsubscribe: majordomo@aros.net "unsubscribe fractal-art"