FOTD -- August 18, 2010 (Rating 7?) Fractal visionaries and enthusiasts: Today's image is a scene in the 'Zexpe' fractal, the Mandeloid created by the formula Z^(epsilon)+C. I think the fractal was given its name by Lee Skinner, who did quite a lot of work with this fractal a number of years ago. The Zexpe fractal rather resembles the cubic Mandelbrot set, though the two main buds are shifted well around toward the negative X-axis. The most interesting part of the Zexpe fractal however lies at the western edge of the main bay, near the X-axis, where all kinds of chaotic things happen. Today's image lies in a phantom valley in a larger minibrot in this chaotic area of the parent Zexpe fractal. It is is a good example of some of the strangeness found there. I named the image "Zexpe Thing", which is what it is. I rated it at a 7?, which is what I think it's worth. The question mark implies that the image might not be entirely of my own creation. The calculation time of 5 minutes is a small price to pay for an enjoyable image. And those pressed for time may always view the finished image on the FOTD web site at: <http://www.Nahee.com/FOTD/> Today's image may owe more to Lee than meets the eye. The image is a zoom into an old image, which I found on a floppy disk that had been stored away for over 10 years. I might have taken that old image from the CD of fractals that came with the second edition of "Fractal Creations". I long ago misplaced that disk. Lee produced many Zexpe images for that CD, and the old image that I found on the floppy disk was created by a formula named 'Zexpe', which I do not have in my files. (I had to make a para- meter file of the original image and edit it so that it would work with the manzpower formula.) The colors are of my own invention however. Now on to what you have all been waiting for -- the weather! Actually, some very pleasant weather prevailed here at Fractal Central on Tuesday, with an azure blue sky decorated with angel- hair cirrus and cottonpuff cumulus clouds, lower humidity, and a temperature of 84F 29C. Nicholas, the oversized all-black gentleman fractal cat, enjoyed the conditions from the top of the secretary, while Cassie, the petite gray lady fractal cat, chose the top of the side-by-side, next to Nicholas. I found my enjoyment in the workroom, where the day's work went unexpectedly smoothly. If all continues going well, the next FOTD will be posted in 24 hours. If not, then look for it anyway. Until then, take care, and when the world ends, will fractals still exist? Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Zexpe_Thing { ; time=0:05:03.10-SF5 on P4-2000 reset=2004 type=manzpower passes=1 center-mag=-0.7104986483027282/+0.077324933946310\ 76/2.344236e+007/1/-97.5/0 params=0/0/2.7182818284\ 5905/0 logmap=381 float=y maxiter=4200 inside=0 colors=000mavnbvnbvobvpcvpcvqcvqdvrdwsdwsewtewuewu\ fwvfwvfwtetsdrrdopcmocknbhnafmacm`am`_m_XkZVjZSiYQ\ hYOlVNoTMrRLrPKrNJrLIrJIrKHrLGrLFrMFqMEnNDlNCiOCgO\ BdPAbP9_Q9YQ8UR7RR6NS6KS5GT4ET4GS8ISBKSEMRHORLQROS\ RRUQUWQXYQ`_PcaPfcPiePmgOpiOskOvmOyXLkHJYMTXRaXWkW\ `tWbnTdhRfbOhXMjRKlLHnFFp9Dn9Gl9Jj9Mh9Pf9Sd9Vb9Y`9\ `Z9cX9fV9iT9lS9n`EhhJcqOYySTxR`wRhtSfrSepScnSblSaj\ S_hSZfSYcTWaTV_TTYTSWTRUTPSTOQTNRRQRQSSPUSOWSNZTM`\ TLbTKdUIgUHiVGkVFmVEpWDrWCtWBvXFpYJkYNfZRaZVX_YR_a\ M`eH`iCam7ap2VtROxoPtnQpmRlmRhlSdkT`kUXjkPUgXpUHdX\ HgXDgWFfKHfUIfTKfSMfRNfQPfPReOSeNUeMWeLXeKZeJ`eIaz\ HczGezFfzEhzDjzDkzCezB_zAVzAPz9Jz8Ez78z73E84F85G96\ H97IA8JA9KB9LBAMCBNCCODDPDEQEEREFSFGTFHUGIVGJWGJXH\ LWLNVPOUUQVZSZcTchVhmXmrYrvXvzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzz9zz9zzAzzBzzDzzDzzFzz\ Izzzzzzzzzzzzzzzzzzzzzzzz } END PARAMETER FILE=========================================
Jim Muth wrote:
Today's image is a scene in the 'Zexpe' fractal, the Mandeloid created by the formula Z^(epsilon)+C. I think the fractal was given its name by Lee Skinner.....
.....and the old image that I found on the floppy disk was created by a formula named 'Zexpe', which I do not have in my files.
Here are but a few of the various "Zexpe" type formulae that may be found within the ORGFORM collection at: http://www.nahee.com/PNL/OrgForm.html Zexpe (XAXIS) { ; Lee Skinner [75450,3631] s = exp(1.,0.), z = Pixel: z = z ^ s + pixel, |z| <= 100 } Zexpe2 (XAXIS) { ; Lee Skinner [75450,3631] s = exp(1.,0.), z = Pixel: z = z ^ s + z ^ (s * pixel), |z| <= 100 } Ze2 (XAXIS) { ; Lee Skinner [75450,3631] s1 = exp(1.,0.), s = s1 * s1, z = Pixel: z = z ^ s + pixel, |z| <= 100 } Zexp2 (XAXIS) {; from ImageLab ; use floating point with this one ?! z=pixel: z=z^1.414213562373 + pixel |z| <= 4 } Zexpe&pi (XAXIS) {; Zexpe with (e + Pi) z = Pixel: z = z ^ 5.859874482049 + pixel |z| <= 100 } Moe { ; Mutation of 'Zexpe'. ; Original formula by Lee Skinner [75450,3631] ; Modified for if..else logic 3/19/97 by Sylvie Gallet ; For 'Zexpe', set FN1 & FN2 = IDENT and P1 = default ; real(p1) = Bailout (default 100) s = exp(1.,0.), z = pixel, c = fn1(pixel) ; The next line sets test=100 if real(p1)<=0, else test=real(p1) IF (real(p1) <= 0) test = 100 ELSE test = real(p1) ENDIF : z = fn2(z)^s + c |z| <= test } ; ; Moe { ; Mutation of 'Zexpe'. --- Original version --- ; ; Original formula by Lee Skinner [75450,3631] ; ; For 'Zexpe', set FN1 & FN2 =IDENT and P1 = default ; ; real(p1) = Bailout (default 100) ; s = exp(1.,0.), z = pixel, c = fn1(pixel) ; ; The next line sets test=100 if real(p1)<=0, else test=real(p1) ; test = (100 * (real(p1)<=0) + real(p1) * (0<p1)): ; z = fn2(z)^s + c ; |z| <= test } Many other collections, such as .PAR, .MAP, .IFS, .L, etc. may be found within the links at: http://www.nahee.com/Fractals/FractInt/index.html Sincerely, P.N.L. -------------------------------------- http://www.Nahee.com/PNL/Fractals.html http://www.Nahee.com/Fractals/
participants (2)
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Jim Muth -
Paul N. Lee