FOTD -- June 30, 2002 (Rating 7) Fractal visionaries and enthusiasts: Today we rise one step out of the rating-of-six rut that we've been mired in for several weeks, all the way up to a rating of 7. The rating seems fairly accurate, considering the unusual textures created by the reference standard outside coloring method of equal iteration bands. Normally, the powers of Z between 0 and +1 do not make fractals, but by using certain tricks, fractals can be coaxed from these powers. One of my favorite methods of getting fractals where none exist is to take the difference between two non-fractal- producing expressions and multiply it by a factor sufficient to create an image. In today's case, that factor is 13. The iterated formula subtracts 13 parts of Z^0.7 from 13 parts of Z^0.75 then adds C. The resulting parent fractal is quite sensitive to its bailout radius. In fact, changing the bailout has such a great effect on today's image that I suspect the entire image might be an artifact rather than a true fractal. But artifact or not, the image is worth being included in that ever-growing list of FOTD's. Studying the image, I was reminded of something that I could not quite remember. Then it came to me. The texture of the fractal elements mimics the texture of algae growing on rocks in a swift- flowing stream not too far from Fractal Central. The name "Algae" soon followed. If the bailout radius of today's image is raised, the picture goes totally black. The image evaporates as all the points become trapped. But then the image can be restored in a new form by setting the logmap to 0 and the inside fill to something non-flat, such as bof61. The 9-minute render time is somewhat slow, but fast relief for rendering pain is available in the form of a download from Paul's web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Saturday here at Fractal Central was not perfect, but compared to how it can be in this part of the world at this time of year, it was good enough. The temperature of 88F 31C, combined with a hot sun, was warm enough for the kiddies to enjoy a splash in their back yard pools, and the humidity was not so high that the more strenuous activities engaged in by adults became unbearable. The cats spent most of the day just being cats and sleeping. As for me, I've got another curious fractal already waiting for the next appearance of the FOTD, which will be on July 2. (Starting in July, I am increasing the frequency of the FOTD to one every even-numbered day.) Until then, I've got the FOTD-CD to work on and a few fun things to do. Until July 2nd, take care, and do the things that need to be done, while ignoring the things that don't need to be done. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Algae { ; time=0:09:33.15--SF5 on a p200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotMix4 function=ident passes=1 center-mag=+0.74222863652301170/+0.608902701512313\ 80/4.102563e+009/1/-125/-1.60218892474028873e-006 params=1/0.75/-1/0.7/12/1600 float=y maxiter=1500 inside=0 logmap=199 periodicity=20 colors=000f0T_0Mo0za3zQJzF_z3oz0zz0yx0ss4mo7gjCagG\ XcJS_OMVSGSVAO_4Jc0Ff0C`39XC7SJ4OS3I`0Dg09p04u06g0\ 6T66FCCL9GP6LV3PX1Tf0Yi0am0fs0jx0oz0pz0pz0ry0ry0rx\ 0sx0sv0sz0uu0uT0vs0Fg0zr0xr0xp0xp0loC`SPPo`Dom1oz0\ zz7izPyzfxvxzpzzlzzjzzjzyjyxjvxirviouijsifricrg_pg\ XogSmgPmgLfiI_jDSjALl6Fd37z00o00p00p30sCcuL3xV7ycD\ zlIzuMzvOxxOpyOjzOczOXzOQzOJzODxSApX7i_4ac1Vf0Tg3S\ i6Qi9PjAOlDMlGLmJJmLVdPfXTrOYzF`zGYyIXxITvJSuLPsLO\ rMLpMJoOGmPFlPCjQAiS7gS6fT3dT1fX3g_3ia4id4jf4li6ml\ 6mo7or7ps7rv9ry9szAuzAuzAuz7sz6sz4sz3vz0xz0zv0zp0z\ j0zf0z`0zX0z`0ucAlfLdjXXmfPppIsz0Ax0Iu0Os4Vr7`pAfo\ FmmIslLyjOziPziSzgTzgXzgYzf`zfazddzdfzdizcjzcmzaoz\ apzarz_syYuvXvsTvpSxmQyjPziMzfLzcJzdIzgFzjDzmCzpAp\ sF`vIJvM3vP6vT7vX9v_AvaCvfDviFvlGvoIvrSvmavilvdvva\ svdpvfmvgjviivjfxlcym`zoYzpXzrTzsQzuOzvMzxPzvSzuVz\ sYzs_zr_zp_zo_zo_zm_zl_zl } frm:MandelbrotMix4 {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(-a*b*g*h)^j, k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END 20.0 PAR-FORMULA FILE==================================