While calculating zooms into the parent fractal of Jim Muth's FOTD for February 6th, 2012, I ran across an especially clear occurrence of something that happens quite often in fractals that I've always found interesting: When two clearly different features or patterns that dominate in their own areas of a fractal meet, often one or the other will "win," and will be the only pattern in evidence in the overlap area, as opposed to creating a mixture of features. I've often wondered what aspect of the mathematics involved makes one feature "win" during these "confrontations." The fractal in question is an anti-aliased zoom into Jim's February 6, 2012 FOTD: F120206A.jpg which I call: "Keep Your Fingers Crossed" I increased Jim's maxiter to 4000 and set color[0] to black to show the confrontation more clearly. I'm going to ask you to click on the fractal's link - "F120206A.jpg" in the far right column labeled: "Hal's Variations on Jim's FOTD (if any)" on my February 2012 FOTD page after navigating to February thru my home page: http://www.emarketingiseasy.com/TESTS/FOTD/jim_muths_fotd.html since I have a counter on my home page, but not on the individual month pages or their images. If your browser resizes the image, be sure to click on it once to see my original pixels, instead of the browser's resampled pixels... Anyone care to venture a thought on what's going on when one feature "wins" during a "meeting" of features in a fractal? Parameter file is below. - Hal Lane ######################## # hallane@earthlink.net ######################## START PARAMETER FILE======================================= A_Mini_What_Is_It2 { ; Hal Lane Feb 11, 2012 t=5:23:31 2.1GHz ; F120206A.jpg 4096x3072 original size, ; anti-aliased 1200 x 900 ; Zoom into Jim Muth's FOTD for ; February 6th, 2012 ; Fractint Version 2004 Patchlevel 4 reset=2004 type=formula formulafile=f120206.par formulaname=julibrotmulti2 function=recip passes=1 center-mag=+0.51016144962107820/-0.69537232287360660/48\ .9205/1/43.0020096674301797/-1.45616946019649474 params=7/400000/167.1/11.4/-125.5/-157.5/-0.1618836541/\ 1.0376863439/-0.1618836541/1.0376863439 float=y maxiter=4000 inside=255 periodicity=6 sound=off colors=000orj<3>nnfnmenld<3>lh`kg_kfZ<2>icWhaUf_SeYPcUM\ bPJ`KGXFCRAEfTG<2>ztK<3>sPMqHMo9Mq0L<8>YDSWFTUGU<2>OLWM\ MXMMV<2>HP_CNc<6>a_MdaKhcH<3>vj8<3>wrWwtawvgyym<8>lgdke\ cicb<3>dWZbX`<3>eRSfQQgOOhNMhLKOSS<3>SZVT`VUbWWaU<8>Slh\ SmiRok<3>QsqhTM<3>nVIoWHpWG<9>WSMURNSRN<3>KQP<3>_IHcGGc\ EE<3>c67<3>c7Dj8E<8>RAPPARNAS<3>EBXCBKABK<7>I7KJ7KK7K<3\

O5K51WO5eU8oUBx<5>UEkUEiUEg<3>UGZpGX<4>nIMmJKmJI<3>kKA\ gLBdLC`g2<15>JFGHDGGCH<2>D6KC5KD7L<8>MOR000 }

frm:JulibrotMulti2 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p2*0.0055555555555556), b=pi*imag(p2*0.0055555555555556), g=pi*real(p3*0.0055555555555556), d=pi*imag(p3*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), aa=-(real(p1)-2), bb=imag(p1), c=p+flip(q)+p4, z=r+flip(s)+p5: z=(bb)*(z*z*fn1(z^(aa)+bb))+c |z|< 6 } END PARAMETER FILE=========================================