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: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> 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 20.0 PAR-FORMULA 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 20.0 PAR-FORMULA FILE==================================