FOTD -- June 11, 2009 (Rating 8) Fractal visionaries and enthusiasts: Today's image is a scene in the Oblate aspect of Seahorse Valley. The Oblate aspect is defined by the real(z) and imag(c) axes of the Julibrot. To find the Oblate view, take the point at -0.75 on the negative X-axis of the Mandelbrot set and imagine the real(z) axis cutting perpendicularly through this point, extending in front of and behind the screen. This line is actually the X-axis of the basic Julia set of Seahorse Valley, and when taken with the real and imaginary C axes defines a three-dimensional hyperslice of the four-dimensional Julibrot figure. Now rotate the 2-D image on the screen 90 degrees around the vertical axis, through this imaginary 3-D hyperslice until it sits in an upright position perpendicular to the screen, facing left and right. This is the oblate aspect of Seahorse Valley. It's easier to think about than describe in words. Now that we have our bearings in Seahorse Valley, what we find in there is a whole slew of those things I call peanut holes. In today's image the holes are filled in because of the maxiter of one-million, but they may be seen in their full glory by lowering the maxiter to 7,500. Curiously, these peanut holes appear in all aspects of Seahorse Valley, while the Mandeloid elements such as minibrots vanish soon after we leave the Mandelbrot orientation. I added superfluous detail to the scene by rendering it with the outside set to 'summ', and then I colored it to resemble a scene on some surreal alien planet. I rated it at an 8 because I kind of like scenes on alien planets. The calculation time of under 10 minutes will probably be cut to less than half on a current S.O.T.A. (state-of-the-art) machine, once the machine is taught how handle the Fractint program. Or perhaps it is best to forget teaching a new computer old tricks, and trek electronical- ly out to the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> to view the finished image in its full glory there. Thickening clouds here at Fractal Central on Wednesday did not dim the spirits of the fractal cats, who spent a good part of the day chasing each other up and down the hallway. The tempera- ture of 84F 29C was just about normal for the end of spring. My day was busy but under control. The next FOTD will be posted in 24 hours. Until then, take care, and does dark energy come from the world of fractals? Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Seahorse_Valley-11 { ; time=0:09:51.37-SF5 on P4-2000 reset=2004 type=formula formulafile=slices.frm formulaname=Oblate passes=1 center-mag=-1.18496393\ 032451400/+0.00512773353588221/33113.21/0.6062/\ -1.06803255737970959/-88.8155012674095872 params=0/0/-0.75/0 float=y maxiter=1000000 inside=0 outside=summ periodicity=10 colors=0001_z1Zz1Zz1Zz1Zz2Yz2Yz2Yz2Yz2Xz2Xz2Xz2Xa2\ W`2WZ2WY2WX3VW3VV3VT3VS3UR3TQ3SP3SO3RM3RL3QK3QJ4OI\ 4OG4MF4ME4LD4KC4KA4J94I84H74H64G56H57H58I59J5AI5BJ\ 5CG5DF5EE5GD5HC5IB5JA5KA5LA5NA5QC5TE5WG5YI5`M5cQ5c\ U5cW5cY5c_5cc5ca5c_5cY5cX5eX5gY5iY5kY5lY5kY5jZ5kZ5\ lZ5mZ5nZ5o_5p_5q_5r_5s_5rZ9rZDrZGrYKrYNrYRrYVrXYrX\ arXdrXhrWlrWorWsrWvqVuqVtpVtpVspVsoVroVroVqnVqnVpn\ VpmUomUnlUnlUmlUmkUlkUlkUkjUkjUjjUjiTiiThhThhTghTg\ gTfgTfgTefTezTdzTdzSczSbzSbzSazSazS`zS`mS_mS_mSZmS\ ZhTZgUZfVZcWZcXZcYZcZZc_Zc`ZcaZcbZccZcdZ`AtZCrYDpX\ FnVHlUJjTKiSMgQOePQcORaMT_LVYKXWJYVIUWHUXGVcGVcFVc\ EVcDWcDWcCWcBWcAWcAWc9Wc8Xb5Ya8ZbA_cC`dEadGbeJcfLd\ gNegPfhRgiThjWijYjk_klalmcmmennhoojpplqpnsqptrrurq\ spprnoqlopjnohmnflmdllbkk`jjZiiXihVhgTgfRfePfdNecL\ dbJ`hHdaHgVHjOHnHHqAHw2Et4Hq5Jo6Ml8Oi9QgATdCVbDY_E\ _XGaVHdSIfPKhNLkKMmIOpFPr } frm:Oblate {; Jim Muth real(z),imag(c) z=real(pixel)+p1, c=flip(imag(pixel))+p2: z=sqr(z)+c, |z| <= 16 } END PARAMETER FILE=========================================