FOTD -- October 23, 2004 (Rating 6) Fractal visionaries and enthusiasts: Today's image takes us to the julfn+zsqrd formula of Fractint, a formula that gave me a fight when I tried to wring a respectful fractal from it. I finally won the battle by investigating the Mandelbrot variations of the formula and finding the parameters likely to produce interesting Julia sets by noting the coordi- nates of the interesting places in the M-sets. Several functions produced interesting Mandelbrot sets. I decided to check the Julia sets associated with the shoreline of the M-set that results when the 'cabs' formula is applied. The first Julia set I checked was a winner. This winning set is an extension in the remaining two dimensions of a point on the the eastern shoreline of its M-set. The set is illustrated in today's image, which shows the entire Julia set, and looks sur- prisingly like yesterday's image. I named today's image "Julia Tree-Rings". I thought of tree rings the moment I saw the image. Such an easily created image can hardly be rated very far above average, but I put a bit of extra coloring effort into the image, and that coloring effort raises it to a slightly-above-average rating of 6. The rings that fill the inside of the Julia set appear very inte- resting as they are. It might appear that they would grow even more interesting as one zooms deeper, but a single inzoom will reveal that they are fractal in nature, and continue dividing into ever smaller similar rings. The rings are ultimately dis- appointing, but they do however produce some interesting patterns in the areas where they converge, and create images much like yesterday's 'moirefan' image. The render time of 6-3/4 seconds is unusually fast, and when com- bined with the rating of 6 results in an overall worth of a grossly inflated 5333. Those who are concerned about inflation can download the image from the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> The weather remained cloudy here at Fractal Central on Friday, but the temperature warmed to 57F 14C and the wind was light, which made things pleasant enough for the fractal cats to enjoy several hours in the yard. Today is starting sunny, and we are promised more sun and warmer temperatures throughout the after- noon. I hope the good weather actually holds up. The cats do not like broken promises. I promised myself an actual day off this weekend, and with only one minor job on the shelf beside the desk, it looks like I'll keep that promise. Luckily, I do not consider playing with fractals to be work. The next playful image will appear right here in 24 hours. Until then, take care, and do palm trees have rings inside their trunks that tell the tree's age? Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Julia_Tree-Rings { ; time=0:00:06.75--SF5 on a P200 reset=2003 type=julfn+zsqrd function=cabs center-mag=-1.249e-016/6.66134e-016/0.8090289/1/57\ .5/1.310757058448075e-014 params=-0.07/0.23 float=y maxiter=1200 bailout=9 inside=0 logmap=yes symmetry=none periodicity=10 colors=0000AN0FT0KZ0PeAUkKZqUckchdmmYvrSzzQmmPccNU\ UMPPKKKJELKIOLNRMRUNOXOM_PKbPHdQFgQDjRBlRIhVOdYV``\ `YcfUgmQjsMmyJpoQnfWlYakPhiGng7tf9ngAhhCbiDXjFRkGL\ kUM`gNQuOFsNGqNGoMGmMGkLGiLGhLGDzXChcBSjABq`Tvzizs\ juljqejmZjiTjeQgiNdmKapHZtFWwGVxHUxITyISyJRzKQzKPz\ QQuWRqaSmgTimUesVayVYJAiG9kD8mB8o87q67sUKTpX2kYAfZ\ IadHXiGSnFOdKKWOGMSCDW84_6AcFHbNNaVU`b__bY_bW_bV_b\ T_bR_bP_bN_bM_`EfZ7lXCkVGjTLiRPhPTgOYgMafKeeIjdGnc\ FrcGs_GsXGtUGtRHuNHuKHuHHvEIvAIw7Iw4Iw1Jv6JvBKvGKv\ LLvQLvVMu_MudNuiNunOusOuwnIKlLLjOMiQNgTNfWOdYPc`Qa\ bQ_eRZhSXjTWmTUpUTrVRuWQwWUqbXli`gpcbvbcubdubetbft\ bgtbhsbhsaisajrakralramqanqanqcondolfojgoghpejpckp\ alpZnpXoqVpqSrqQsqOtqMonOjkQehS`eUXcWS`YNY_IVaETbF\ WcGYcG_cHacHccIfcJhcJjdKldKndLqdMsdMudNwdNydQtbTp`\ WlZZhYadWd`UgXSiTRoCkkGjgKjcOj_SjWWjS_jOciKgiGkiCo\ i8si5wi7vk9ulAHb9MZ8RV7WR } END PARAMETER FILE=========================================