; Date: Mon, 22 Sep 2008 18:01:20 -0400 ; ; To: fractint@mailman.xmission.com ; ; From: Jim Muth ; Reply-To: Fractint and General Fractals Discussion ; ; ; Subject: [Fractint] FOTD 23-09-08 (Safe at Home [7.5]) ; ; Id: <1.5.4.16.20080922180238.2b0fff7a@pop.mindspring.com> ; --------- ; ; FOTD -- September 23, 2008 (Rating 7.5) ; ; Fractal visionaries and enthusiasts: ; ; The fourth dimension is all around us, but because we look in ; the wrong direction, we can't see it. Then we protest that ; there are no more directions out there for us to look in. And ; this explains the difficulty. Instead of looking out there, we ; must look within, into our minds, which is where the fourth ; dimension, whatever it is, intersects our three-dimensional ; space. ; ; After years of looking within, I have created a mental four- ; dimensional hyper-planet, which I sometimes explore when sleep ; eludes me. Exploring this planet one 3-D section at a time is a ; far more efficient way of falling asleep than counting sheep. ; ; Sometimes, while traveling around the equator of my hyperplanet, ; I can almost form an image of the whole hypersphere. As I ; progress westward, I can see the polar great circle, which is ; the axis of rotation, appearing to turn on itself, all points of ; it always 90 degrees from wherever I may wander on the equator. ; ; At the same time, the equator can be the axis of rotation of the ; polar circle, resulting in the strange motion known as double ; rotation, a motion that can exist only in spaces of four or more ; dimensions. I am not sure what would be the apparent motion of ; the heavenly bodies as seen from the surface of a 4-D planet in ; a state of double rotation, but I suspect it might resemble a ; 3-D helix. ; ; One thing totally certain is that today's image has a minibrot ; at the center, and lies in the fractal that results when the ; formula Z^(1.9)+C. is iterated 8.7 turns up the logarithmic ; ladder with no function applied. ; ; When I named the image "Safe at Home", I might have been ; thinking of the Orioles baseball team, which I still listen to ; on the radio. I was definitely thinking of the coloring when ; I rated the otherwise humdrum image at a 7.5. ; ; The calculation time of 1-2/3 minutes will give the eager ; fractalist little time to think of anything else. And as ; always, the finished image is posted on the FOTD web site at: ; ; ; ; Persistent clouds blocked the sun here at Fractal Central on ; Monday, but the temperature of 70F 21C was near ideal. The ; fractal cats must have agreed, for they spent an unusually long ; time on their shelf in the side window, watching for any stray ; cats that might wander by. ; ; My day was rather good. The work was out of the way just after ; lunch, and the fractal is at least adequate. The next FOTD will ; be posted in 24 hours. Until then, take care, and live life in ; the hyper-reality of 4-D. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= Safe_at_Home { ; time=0:01:39.33-SF5 on P4-2000 reset=2004 type=formula formulafile=allinone.frm formulaname=MandelbrotBC3 function=ident passes=1 center-mag=+0.6619148328728458/-0.66194260281007/\ 2.045298e+010/1/-100/0 params=1.9/0/8.7/0 float=y maxiter=2200 inside=0 logmap=147 periodicity=10 colors=0000300400500600700800901A02B03C04D05E06F07\ G08H09I0AJ0BK9CLEDMIENLFOOHRRIUUKXZL_cNahOdmQgrRjv\ TmzUpzWszXpzQmzKezDWz7Sz6Qz6Nv6Kr6Gm6Eh5Bc58Z56U53\ P51L83JB4IE5HH6GK8FM9EPADSBCVDBYEA`F9mG8rI9vJ9zP9z\ U9zZ9zP9zQ9wR9mNEcIIUDMTDQTIUTNYSSYSSUSSURSURSURKU\ PKUNKUMKUKKUJKUHKUFKUEKUCSUBRUFSUJTUNUURUUVVTZWTbX\ SfXRjYQnZPqZPnXTkVXiT_fRccPgaNjZLnWJrUHuSJqQLmONiN\ OfLQbJSZHUVGVSHXQIYOIZMJ`KKaJKbHLcFMeDMfBNgAOh8Oj6\ Pk4Ql2Qm1Pj2Oh2Ne2Mc2M`2LZ2KX2JU3IS3IP3HNzGKzFIzFG\ zBCz79z46z3Gz2Qz1_zkNz_TzOZzCdza3zJPzIFziQzVXzGcz`\ qzc7zRKzEXzcYzShzyUzd_zLdztezffzTgzFhzc5zKQzVozLmz\ BkzY`zTezUYzVQzWIzXBz`CzdDzhDzbCzYCzSCzNCzMGzMKzMO\ zl_z`bzJgzPdzDgz2jz1izAGzZ0zINzjXzvmztlzfkzTjzFizE\ IzAPz7Wz4bzGHzCPz8Wz4bzr9zdJzSSzE`zMAzBSzd_zVbzLdz\ BgzyWzOMzISzCYz6cz5Uz8Cz4TzLhz15z1QzKkzFjzAjz5izpn\ zLazEdz7gz5`z3ezkjzmlzpoz } frm:MandelbrotBC3 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)+PI-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|