FOTD -- August 13, 2014 (Rating A-5,M-8) Fractal visionaries and enthusiasts: Today's formula is another new one: ------------------------------------------------ BranchCutGenJul { ; Jim Muth Z=Pixel, C=p2: Z=log(Z), Z=exp(real(p1)*(Z+flip(imag(p1))))+C, |Z|<100 } ------------------------------------------------ The formula is a Julia version of the 'BranchCutGen' formula. The image shows a variation of our old friend, the strange open rectangle in the Julia sets of the Z^(2.003)+C Mandeloid. The rectangle itself, distorted and partly filled in, fills the entire screen. The name "Rectangle Regress" refers to the infinite regress in the image. Such regress is quite common in fractals, and in today's image appears as the smaller rectangle just northeast of the center of the large rectangle. This smaller rectangle is an exact copy of the larger rectangle, and has an identical but even smaller rectangle near its center. The process continues to the limit of resolution. The art rates an average everyday 5. The math rates a slightly liberal 8 because of the regress and also because of the new formula, The calculation time of one minute should cause no problems, but the web sites are always there to eliminate the calculation hassle. The image has been calculated and posted to the FOTD web sites at: <http://www.crosscanpuzzles.com/Archives.html> <http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html> <http://www.Nahee.com/FOTD/> <http://user.xmission.com/~legalize/fractals/fotd/about.html> After 3 inches, 7-1/2cm, of rain yesterday, today was a great improvement. The partly cloudy skies and temperature of 79F 26C were just what the doctor ordered. The conditions must have been just what the fractal cats' doctor ordered also. They spent most of the day at the windows watching the birds and the occasional passing squirrel, while the humans watched the work. The next FOTD will be posted within a reasonable time. Until reason prevails, take care, and the less the entropy the better the situation. Jim Muth jimmuth@earthlink.net START PARAMETER FILE======================================= Rectangle_Regress { ; time=0:01:00.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=BranchCutGenJul center-mag=+0.00122607\ /+0.07382828/260/1/-23.75/0 params=2.003/0.0001/\ -1.7435/0.0001 float=y maxiter=1500 inside=0 logmap=79 periodicity=6 colors=000d_WbaY`c_ZeaXgcVieTkgRmiPokIrkOplUnlZlld\ jmihmofmtdmthjtlhtpftsdnm_igVdaQ_WLUQGPKBKE6F81A92\ A93A94A95A96A97A98AA9AAAAABAABAACAADAAEABFABGABHAB\ IABJABKJ7NXBKiEHvHEnGMgGUbE_`G`ZIaXKbWMcUOdSPdQReP\ TfNVgLXhKZiI_iGajEckDelBgm9in6no8jn9gmAclB`lCXkDUj\ EQjFNiGJhGFiHGhIHhJIgKIgKJgLKfMKfNLfOMeONePNdQOdRP\ dSPcSQcTRcUSbVSbWTaWUaXUaYV`ZW``XbZW`YVZWUXVUVUTTS\ SRRSPQRNOQLNPJMPHKOFJNDFMBINBKOBMPBOPBQQBSRBURBWSB\ ZTB`UBbUBdVBfWBhWBjXBlYBnYBmYDmYEmYGmYHmYIlYKlYLlY\ MlYOlYPlYQkYSkYTkYUkYWkYXj__kYYkWWlUUlSSlQRmOPmMNn\ KLnIJnGIoEGoCEpACp8Ap69o9AnBAmDBmFBlHBkJCkLCjNDiPD\ iRDhTEgVEfXFfZFe`FdbGddGcfHbhHbjHalI`nIasF`pI`mK`j\ M`gO`dQ_aS_ZU_XW_UZ_R`ZObZLdZIfZFhZCj`BkZAlXAlWAlU\ AlSAlRAlP9lO9lM9lK9lJ9lH9lG8lE8lC8lB8l98l83o88l8Ci\ 8Hf8Lc8Q`4WX8UZCS`FQaJOcMMeQLfTJhXHi`FkcDmgCnjApn8\ rOlZZwIVjQRYYOLdUQa_VZfYU } frm:BranchCutGenJul { ; Jim Muth Z=Pixel, C=p2: Z=log(Z), Z=exp(real(p1)*(Z+flip(imag(p1))))+C, |Z|<100 } END PARAMETER FILE=========================================