FOTD 25-11-04 (Analemma [7])
FOTD -- November 25, 2004 (Rating 7) Fractal visionaries and enthusiasts: Today's image takes us to the next formula in line, the 'newton' formula, which works the same as the 'newtbasin' formula except that it colors the images according to the number of iterations it takes for the iterated points to reach their roots. For some arbitrary reason, I named the image "Analemma". An analemma is the figure-8 graph usually seen in the Pacific Ocean areas of world globes. At a single glance it shows the sun's declination and the equation of time for each day of the year. But there is little in today's image that resembles an analemma. The word simply seemed to fit the mood of the moment when I thought of it. The image itself resembles a solar eclipse more than anything else. Or some might see a steering wheel at the center. It is an unusual picture when compared to my standard routine of an unending string of images with decorated Mandelbrot midgets at the center. But since starting the tour of the Fractint formulas, I have done many images with no midgets, so maybe today's image is not so unusual after all. I created the picture by setting the single parameter to a rather high value of 240 and rendering the scene with the outside set to 'mult'. Apparently just for the fun of it, the 'mult' option colors the pixels by multiplying the iteration count of escaping points by their real divided by maginary values at the time they escape. The render time on my ancient worn-out machine is a nominal 12-3/4 minutes. This joins with the rating of 7 to give an overall worth of 55. For those who do not render, the image is available for download on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> Those who download from the web site can ignore the overall worth. An off-and-on light rain fell all day Wednesday here at Fractal Central. The rain did not amount to much, but it was enough to keep things wet and keep the fractal cats confined indoors. Luckily we were well stocked with tuna. Today is starting partly cloudy and quite mild, but showers are in the area, and the wind is rising. The cats have yet to pass judgement on the conditions. In my department the work is caught up and I have little to do for the rest of the day but take it easy. So far I have heard nothing about being invited to any dinners. Unless something changes, this will leave me plenty of time to find the next fractal. Until that next fractal appears, which will happen right here in 24 hours, take care, and then take further care. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Analemma { ; time=0:12:47.53--SF5 on a P200 reset=2004 type=newton passes=1 center-mag=0/0/0.1\ 261867 params=240 float=y maxiter=7500 bailout=9 inside=0 outside=mult logmap=yes symmetry=origin periodicity=10 colors=000000zzzzzzzm4zm6zm7zm8tKgrMhqNhpPhoQhnShl\ TikVijWiiYihZif`jeajdcjcdjbfj`gk_ikZjkYlkXmkYljZkj\ Zjj_ij_hj`gjagjafjbejbdjccjcbjdajeaje`jf_jfZigYigX\ ihXiiWiiVijUijTikSikRilRimQimPinOinNioMisKjqLipLio\ MinMhmNhlNhkOgjOgiPghPggQffQfeRfdRecSebSe`Te_TdZUd\ YUdXVcWVcVWcUWcTXbSXbRYbQYaPZaOZaN_`M_`K``J``Ia_Ha\ _Gb_FbZEcZDcZCdZBdYAeY9eY8fX7fX6gX3iW4hX4hX5gX5gX6\ fY6fY7eY7eY8dY8dZ9cZ9cZAbZAb_Aa_Ba_B`_C`_C_`D_`DZ`\ EZ`EYaFYaFXaGXaGWaGWbHVbHVbIUbIUcJTcJTcKScKScLRdLR\ dMQdMQdKSbLRcMQdMQeNPeNPfOOgOOhPNhPNiQMjQMkRLkRLlS\ KmSKnTJnTJoUIpXHtWIrVIqUIpTInSImRIlQIjPIiOIhNIfMIe\ LIdKIbKIaJI`IIZHIYGIXFIVEIUDITCIRBIQAIP9IN8IM8ILAH\ NCGPEFRGETIDVJCWLBYNA_P9aR8cP4fS7dUAbWC`YF__HYbKWd\ NVfPThSRkTSjURjURjUQjUQjUQjUPjUPjVOjVOjVOjVNjVNjVN\ jVMjWMjWLjWLjWLjWKjWKjWKjXJjXJkYKlZKm_Kn`KoaKpbKqc\ KrdKseKtfKugKvhKwiKxjKykK } END PARAMETER FILE=========================================
On Thu, 25 Nov 2004, Jim Muth wrote: (...)
Apparently just for the fun of it, the 'mult' option colors the pixels by multiplying the iteration count of escaping points by their real divided by maginary values at the time they escape. (...) In the C languaje is the possibility of branching on the results of an assignment. That is, you can write (z=c) and perform a certain function if the assignment happened to clear zed, that is to make it zero.
The sheer variety of coloring options makes me want to sujest a way to put the enumerated functions (atan, atanh, etc.) into the z-screen, where there are already a lot of options for determining when an escape will occur. Perhaps, also, there could be a function applied to zed after an escape and before the color number is determined, allowing you to put the absolute value of zed into the real part of zed before FracTint determines the colour. In other words, the user might opt to apply the natural logarithm to zed before fractint's own logmap feature is applied to the number for the colour. _______ In Mathematics, there is never a bigger half. There is always a bigger half in Physics.
participants (2)
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brewhaha@freenet.edmonton.ab.ca -
Jim Muth