; Date: Mon, 11 Oct 2004 10:11:17 -0400 ; From: Jim Muth ; Subject: [Fractint] FOTD 11-10-04 (The Right Root [5]) ; Id: <1.5.4.16.20041011101217.392fff10@pop.mindspring.com> ; --------- ; ; FOTD -- October 11, 2004 (Rating 5) ; ; Fractal visionaries and enthusiasts: ; ; The Newton formulas are not really escape-time formulas, but ; they work in much the same way. Today's image was created by ; the complexbasin Newton formula. This formula uses Newton's ; method of finding roots, and colors the points according to ; which complex root they converge on. ; ; In the Newton's fractals, much of the interest lies where areas ; of different colors appear to touch. The different colors do ; not actually touch however, they merely exist close to each ; other. At every color boundary a fractal pattern exists that ; separates the colors. This pattern exists even at the smallest ; scales. ; ; Since I have done very little exploration in the Newton's ; formulas, I am not familiar with the things they can do. They ; certainly can do more than I have done with today's image, where ; I have used negative and imaginary parameters, and rendered it ; with the outside set to 'fmod'. Even the little bit I have done ; rates a 5 however. ; ; Maybe when my tour of the built-in Fractint formulas is ; finished, I will return to the Newton's formulas for further ; exploration. I can see by the sharp cut in the image that it ; is but one level of an infinite spiral, much like the branch- ; cut fractals I often work with, though in this case, it appears ; that the unseen levels would appear similar. ; ; All things considered, I rated the image at a 5. I named it ; "The Right Root" for no particular reason. Due to the render ; time of only 19 seconds, the rating of 5 leaps to an incredible ; and grossly inflated 1534. The completed image is or soon will ; be available for download on the FOTD web site at: ; ; ; ; The perfect weather here at Fractal Central on Sunday kept the ; cats relatively happy. They would have been perfectly happy if ; we had not gone out in the afternoon and brought them inside. ; But half a perfect day is better than no perfect day, and when ; we returned in the evening, they ran to greet us as eagerly as ; ever. Today is starting almost perfect. Only a chilly tempera- ; ture of 48F 9C is keeping it from being absolutely perfect. ; ; For me, being caught up in the commercial work leaves that much ; more time for fractal work. The next fractal will appear in 24 ; hours. Until then, take care, and be on the lookout for the ; fractal UFO's. ; ; ; Jim Muth ; jamth@mindspring.com ; jimmuth@aol.com ; ; ; START PARAMETER FILE======================================= The_Right_Root { ; time=0:00:19.56--SF5 on a P200 reset=2003 type=complexbasin passes=1 center-mag=-0.174754/-1.0781/0.5577863/1/137.5/-2.\ 50563458870090017e-014 params=-6.3/2/-0.5/0 float=y maxiter=500 bailout=9 inside=bof61 proximity=3 outside=fmod periodicity=0 colors=O0U0zzPkSQlUSnXTq_Ur`YlhagofawiXzdaw`grWllS\ qgMu`HzWAzP5zIMzPYzTkuXur`tratrctrdsrfsrgsrhsrhrri\ rrkrrlqrmqrnqronzmownqrormqshqtcruYszYroNtyHuzAwz6\ zz5zz5yz5wx5ut2sr2ro2om2ni0lg0kd0ha0g`6f_Cd_HdYMcX\ QcXUaWY`Ua`hzPizNizMizKizKizIizHizFixFizDisCihAioA\ hmCgkDfhFdfHccIa`KaYK`WM_TNYQPXNQWKSQI0TH6UHHWHSXH\ _YFh_Fo`FxU5zX8z_CzaFzcIzfMzhPzkSzlUznXzq_zsaywXzu\ _zuaztcytfwshtsiqrlnmrfoohqnkrmltlnukqwiryhtzfwzdx\ zczzazz`zz_zzYzzXzzUzz_zzKuq6muNlsMgoKamIXiFSgDMcC\ F`A8YCFWCMTCSQCWNC`MDfIDkFDnCDs8Dx06z6DzDIzIPyPTxT\ YwYawagugktkososruuttwsswrsxrrxqqyoqyooznnzmnzmmzl\ ozrnzonzmmzlmxiltglqfkmclddkgckhakiakl`km`kn_koYir\ YisXitXiuWixUiyUizTizTgnKd`A`F0cM0dQ5gWAh_DkdIlhMm\ lQoqTqtXsy_tzctzduzfuzgwxhwthxqixlkxhkydly_mzWnzSn\ zMozHqz0zz5xz8tzCqzFmyKiwNfuQ`sTXrXTq_PnaKmdFYIDui\ 8lgAcfCTcDH_CIaFKdIMfMNhP } ; END PARAMETER FILE========================================= ; ;