FOTD -- December 11, 2004 (Rating 8) Fractal visionaries and enthusiasts: I have always enjoyed pictures that show imaginary but possible scenes on other planets circling other stars. Today, thanks to the HyperMandelbrot formula, we have a star-like 'brot' rising above the floor of an imaginary valley on an imaginary planet in Fractal Land. After a bit of consideration, I named the image "Brot Rising". The word 'brot' does not refer to food. It is a word I invented to describe a fractal feature that shows the typical Mandelbrot- type buds and is likely to hold intact midgets. True, the bud in today's image is partly concealed by exotic alien clouds, and I doubt that it holds any intact midgets, but it comes close enough to the shape of a Mandel bud to earn its name. The scene itself exists in the four-dimensional hypercomplex Mandelbrot set, which itself is a single four-dimensional slice of an eight-dimensional monstrosity known as the hypercomplex Julibrot figure. Unlike the more familiar four-dimensional Julibrot, parts of which I can visualize, this Julibrot is totally beyond my woefully limited power of visualization. But a bit of rather simple math will show that through any of its points there passes: 1 stand-alone 0-dimensional point 8 mutually perpendicular 1-dimensional lines 28 mutually perpendicular 2-dimensional planes 56 mutually perpendicular 3-dimensional spaces 70 mutually perpendicular 4-dimensional spaces 56 mutually perpendicular 5-dimensional spaces 28 mutually perpendicular 6-dimensional spaces 8 mutually perpendicular 7-dimensional spaces and 1 stand-alone 8-dimensional space The series reminds me of Pascal's triangle. The image rates an 8, mostly because I like other-worldly scenes. It renders in 2 minutes, which is fast enough to earn it an overall worth of 393. It may be donwloaded in somewhat less time from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The temperature reached 50F 10C, but persistent light rain fell all day Friday here at Fractal Central. The cats passed the day alternating between sleeping on the couch and sitting on their shelf by the window, watching the rain. Extra tuna kept them happy. This morning is starting cloudy with more rain. The day probably will go no better for the dynamic duo. For me, the day appears as though it will be slow, which only increases the chances of a great fractal for tomorrow's FOTD. Check then to see how great. Until next time, take care, and rise with the buds. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Brot_Rising { ; time=0:02:01.99--SF5 on a P200 reset=2004 type=formula formulafile=allinone.frm formulaname=HyperMandelbrot passes=t periodicity=0 center-mag=-0.166657/0/5.940446/1.1211/-90/3.88578\ 058618804789e-016 params=1.03/0/5/0/1e-008/0 float=y maxiter=2500 inside=255 logmap=yes colors=000FJHHGHJEHKBHL9HPHHRJHULHWOHZRHaVHdZHfaHi\ eIlhJolJqoJ9NcAMcBLcCKcDJcEIcFHcGGdHFeIEfJDgKChLBi\ LAjL9jK8jL9jMAjMAjNBjNCjOCjPDjPDjQEjQFjRFjSGjSGjTH\ jTIjUIjUJjVJjWKjWLjXLjXMjYMjZNjZOj_Oj_Pj`PjaQjaRjb\ RjbSjcSjcTjdUjeUjeVjfVjfWjgXjhXjhYjiYjiZjj_jk_jk`j\ l`jlajmbjmbjncjocjodjpejpejqfjrfjrgjshjshjtijuijuj\ jvkjvkjwljwmjwljwljwljwliwkiwkhwkgwkgwkfwjfwjewjdw\ jdwjcwicwibwiawiawi`wh`wh_whZwhZwhYwgYwgXwhXwhWwiV\ whVwhUwiUwiTwiSwiSwiRwiRwiQwiPwiPwiOwiOwiNwiMwhMwh\ LwhLwhKwhKwiLwiMwiMwiNwiOwiOwjPwjPwjQwiRwiRwiSwhSw\ iTwiUwiUwhVwhVwhWwiXwiXwhYwhYwhZwh_wh_wi`wi`wiawib\ whbwhcwhcwidwiewiewifwifwigwjhwjhwjiwjiwjjwjkwjkwk\ lwklwkmwknwknwkowkowkowlowlowlowmpwmpwmqwnqwnrwnrw\ oswoswotwptwpuwpuwqvwqvwqwwrwwrxwrxwsywsywszwszwsz\ wszwszwszwszwtzwtzwtzwtzwuzwuzwuzwuzwuzwuzwuzwuzwu\ zwuzwuzwuzwuzwuzwuzwuzzz` } frm:HyperMandelbrot {; periodicity must be turned off a=(p1),b=(0,0): q=sqr(a)-sqr(b)+pixel, b=(p2+2)*a*b+p3, a=q, |a|+|b| <= 100 } END PARAMETER FILE=========================================