Hi, Jim, While it may not seem like it at times, it's important to remember that most human interactions are positive. The negative have more visibility and their affront has more impact than a single good act - a dozen people can smile at you as you walk down the street and one person snarling at you can make you feel worse than the dozen smiles made you feel good - but it's too easy to let that lead you to think the world is worse than it is. And for those of us out here on the receiving end, the arrival of a lovely and/or fascinating FOTD is one of the bright lights we look forward to. I hope you can hang in there and keep lighting up the world. Mike On 06/12/2014 11:13 PM, Jim Muth wrote:
FOTD -- December 05, 2014 (Rating A-?,M-8)
Fractal visionaries and enthusiasts:
I am thinking of (but not decided on) putting the FOTD on hiatus until after the holidays or even until the current social unrest calms down for good. Well, maybe I'll slip in an occasional image every few weeks so those still fascinated with fractals, if any, will not be thrown into sudden withdrawal.
It's kind of hard to enjoy fractals and fractal math while swimming in a sea of such unbounded human stupidity and inexcusable blindness. But, for today at least, we have one more, and I hope not the last, venture into the four-dimensional Z^2+C Julibrot.
Today's image is named "Threads of Valleys". This is because it has parts of both Seahorse Valley and Scepter Valley in it. Scepter valley appears as the brilliant short ragged vertical thread on the left, Seahorse Valley is the longer smoother thread on the right. A bit of the large minibrot on the main stem of the M-set is also visible.
The view is what would be seen if the Mandelbrot set were viewed from above, filled out in a particular third dimension. The X-axis of the image is the real(C) axis of the Julibrot; the Y-axis is the direction halfway between the imag(Z) and real(Z) axes.
Since I made almost no effort to work on the art aspect, I gave the image no art rating, leaving it to the interested viewer to apply his own rating. The math rates an 8 because, even though the math trick is over a decade old, I still find it fascinating.
The calculation time of 15 seconds simply means that the image is basically instantaneous. But as always, the web sites can make things even simpler.
The finished image, for what it is, may be viewed online at:
<http://www.crosscanpuzzles.com/Archives.html>
<http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html>
<http://user.xmission.com/~legalize/fractals/fotd/about.html>
Lots of clouds, a temperature of 39F +4C and a little light rain made today one to be forgotten here at Fractal Central. The three fractal cats had forgotten the day by the time it was an hour old. The next FOTD will be posted sometime in the future, but no promises are implied. Until next time, whenever that might be, take care, and can't anyone see what's going on?
Jim Muth jimmuth@earthlink.net
START PARAMETER FILE=======================================
Threads_of_Valleys { ; time=0:00:15.00 SF5 at 2000MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=slicejulibrot4 passes=1 center-mag=0.0559808/0/0.83 params=45/90/0/1.965/\ -0.75/0.04/0/0/2/0 float=y maxiter=1500 inside=0 logmap=1 periodicity=6 colors=00004C06D08F0AG1DH2GL3KO4OR5SU6WX7__8bbAeeC\ hhEkkGnnIqqKttMwwiyzkzzmzzozzpzzrzztzzvzzwzzszzozz\ kzzgzpczn_zlWzkSziOzgKzeGzdCzb8z`FwS5t_7p`8l`Ah`Bd\ `zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz\ zzzzzzzzzzzzzzzzzzzzzzzzz }
frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^(real(p5))+c |z|< esc }
END PARAMETER FILE=========================================
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