; Date: Wed, 27 Aug 2003 10:35:30 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 27-08-03 (An Actual Spiral [6]) ; Id: <1.5.4.16.20030827103555.38ef89c8@pop.mindspring.com> ; --------- ; ; FOTD -- August 27, 2003 (Rating 6) ; ; Fractal visionaries and enthusiasts: ; ; In yesterday's FOTD I stated on a hunch that the valley in which ; the scene is located contains no spirals. Shortly after I sent ; off the FOTD, I returned to the valley in question and found, ; you guessed it, spirals beyond counting. The features in the ; valley that truly have no analog in the classic M-set are the ; wedge-shaped areas that appear hanging from everything in sight. ; And I'm not too sure even of this. ; ; Today's image pictures one of the valley's cubic midgets, and as ; is obvious, the midget is surrounded by a well-defined spiral. ; In the world of fractals, as in the everyday world of material, ; one must never make assumptions unless those assumptions are ; based upon solid evidence. Yesterday, I spoke before I checked; ; today I admit my error. ; ; I have on the shelf across the room an old text book of the ; principles of physics, which was published in 1884. When I make ; assumptions that prove to be wrong, I sometimes console myself ; by opening this book to the lengthy chapter on "ether waves", ; which we now call electromagnetic radiation. The book was ; written at a time when the luminiferous ether was still assumed ; to exist, but experiment after experiment was showing that the ; ether concept led to unsolvable paradoxes. ; ; Today, the contrived explanations and many interpretations that ; were in favor back then seem almost comical in their implausibil- ; ity. Not only does the beleaguered scientific doctrine of that ; long-past period enable me to feel less embarrassed over my own ; mistakes, but it shows how the efforts of even the most devoted ; and rational scientists can be frustrated by their refusal to ; let go of comfortable old beliefs. ; ; At the present time, quantum theory is in much the same state as ; was the ether theory 120 years ago. Competing interpretations ; abound. The problems with the theory of ether were solved when ; a genius called Einstein put all the puzzling theories and exper- ; iments together and came up with the theory of relativity, which ; immediately solved the paradoxes by showing that they were based ; on wrong assumptions, and therefore did not really exist. I ; wonder what genius will solve the present-day quantum paradoxes ; and open our eyes in much the same way as Einstein did nearly a ; century ago. ; ; Before getting totally sidetracked, I should tell that today's ; image is one of an actual spiral, and that is what I named it. ; The rating of a routine 6 seems about right for the scene, which ; has really nothing unique in it. The render time of 12 minutes ; is a bit slow for such an image, the likes of which has been ; seen numerous times before. But this 12 minutes can be cut ; drastically by downloading the completed GIF image from Paul's ; web site at: ; ; ; ; or from Scott's site at: ; ; ; ; If you get no response from Scott's site, try again later. His ; server may be down temporarily. ; ; The Tuesday temperature of 86F 30C was pleasant enough here at ; Fractal Central, but light rain at midday and a severe wind and ; rain thunder-squall at 5pm put a damper on the dynamic cats' ; day in the outdoors. An evening treat was needed to restore ; their good moods. ; ; Tuesday brought no unusually good events for me, but it also ; brought nothing serious to complain about, so I'll consider it ; an uneventful day, which is really all one can ask for. We'll ; try to have another uneventful day today. Until 24 hours from ; now, take care, and the best is always yet to come. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE================================ An_Actual_Spiral { ; time=0:12:31.93--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XY-ZW-new function=ident/flip passes=1 center-mag=+0.0009171456857348/+1.0933816\ 55554275/1.554455e+011/1/-19.9998367841645539/-1.6\ 467749071533144e-006 params=0/0/3/0/0/0/0/0 float=y maxiter=3200 inside=0 logmap=538 periodicity=10 colors=000ctzctzctzctzctzctzctzctzctzctzctzctzctzc\ tzctzctzcszcqzcpzclzcizcizcizciz_iz_gzbdzgawl_spXp\ tTlzRizOfzLbzK_zPXzUTzXQz_NzaJzZGxUGtPIsKIqFIpEJnE\ JlDJkDJgDLfDLdBLbBNaBN_BNY9NV9OT9OR9OQ8QO8QN8QL8QN\ 9QN9QNBQNBQNDQNDQNEQOEQOEQOGQOGQOIQOIQOJQQJQQJQQLQ\ QLQQNQQNQQOQQOQRQQRRQRRQRTQRVQRXQRXQTXQT_QT_QTaQTa\ QTdQTdQVfRTdQTfQTfQTfQTfQTfQTgQTgQTiQTkQTlQTnQTpQT\ qQRsQRtQRwQRwQRzQRzQRzQRzQRxORwORtORsORqORpORnOQlO\ QkOQiOQgOQfOQdOQbOQaOQ_OQYOQYQQYRQYTQYVO_XQYYQX_QX\ aQVbQVdQTfQTgQRiQRkQQlQQnQOpQOqRNsRLtRLwRJxRJzRIzR\ IzRGzRGzREzREzRDzQBzRDwTDsVDpXDlYDi_DfbGbfJ_iNXlQT\ pTQsXNw_JzbGzfDzi9zl6zp4zt9zzDzzGzzJzqNziQzaTzTXzL\ _zDbzDfzDizDlz6nq1si0wa0zT0zL0zD0z40z00z20z60z90zB\ 0zE0zI0zL0zO0zR0zV0zX0z_0zb0zf0zi0zl0zp0zq0zt0zx0z\ z0zz0zz1zz1zz1zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0\ zz0zz0zz0zz0zz0zz0zz0zz0z } frm:multirot-XY-ZW-new {; draws 6 planes and rotations ;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J ;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3, c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4: z=z^(p2)+c, |z| <= 36 } ; END PARAMETER FILE================================== ;