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: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> 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|<a } END PARAMETER FILE=========================================