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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today, with the aid of the SliceJulibrot2 formula, we enter 4-dimensional hyperspace. Hyperspace is any space of more than 3 dimensions. I confine my investigations to 4-dimensional hyperspace, which we can come the closest to visualizing with our 3-dimensional brains. The formula draws most slices of the 4-dimensional Z^2+C Julibrot figure. Being unable to visualize all possible orientations in 4-D hyperspace, I will not claim the formula draws every possible orientation, but I have not yet found a slice that it cannot draw. Today's slice is orientated close to the Parabolic direction, but rotated 1/3 of the way toward the Elliptic direction. As should be evident from the elements that resemble goofy eyes, the scene is located in the East Valley area of the Mandelbrot set. There are no 'inside' areas appearing in the image. The area that resembles a blue sky with patches of haze is actually composed of very high iteration 'outside' stuff made more interesting by being rendered with the outside=imag option. The picture vaguely resembles a scene on an alien planet, which is why I named it "Alien landscape". The rating of a 5 shows that I am not thrilled with the result. The render time of 5-1/2 minutes is fair enough. Rendering may be totally eliminated by downloading the finished image from the FOTD web site at: The report is that the weather was uneventful at Fractal Central while we were away over the week-end. The ice-storm stayed well out of our way to the west and south. We found one possible home for the new Fractal Central, but it has problems that would need to be worked out. My sister reports that the fractal cats seemed unconcerned that fractal lady and I were gone for two days, though they were concerned that their accustomed tuna, might not be served on time. They also demanded that they be allowed to check the weather for themselves. The next FOTD will likely appear in 24 hours. ( I will no longer say certainly.) Until then, take care, and not even the appearance of the FOTD fractals, is absolutely certain. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Alien_Landscape-2 { ; time=0:05:31.48--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=SliceJulibrot2
center-mag=+0.25000501074059570/-0.051641324143515\
65/4.739839e+008/0.04713/-156.857105609805927/65.4\
90051767333938 params=30/90/0/0/0/0/0/1 float=y
maxiter=500000 inside=0 outside=imag periodicity=10
colors=000jrWirVhrVgrUfrUfrTerTdrScrSbrRbqRaqQ`qQ_\
qPZqPZqOYqOXqNWqNVqMVqMUqLUqLUqKUqKUqKUoJUmJUlIUjI\
UhHUgHUeGUcGUbGT`FTZFSYESWERUDRTDQRCQPCPOCPMBPKBPJ\
APHAPF9PE9PC8PA8P98PB9PDAPFBQHBRJCSLDUNEZPETQFNRGH\
TIBUJ5VKSbSmi_nhVngQogLofGpfBpe6pe2nf6lf9kgCigFghI\
fhLdiOciRajU_jYZk`XkcWlfUliSmlRmoPnrOnuQmsRlqSkoUj\
mVjlWijXhhZgf_gd`fcaeacd_ddYecWfbVhaTi`Rj`Pl_NmZMn\
YKoYIqXGrWEsVDtVBvU9wT7xS5yS4wQ5uP6sO7qM8pL9nKAlIA\
jHBiGCgEDeDEcCFbAG`9GZ8HX6IW5JU4KS2PQ1UP6ZOCcOHhOM\
mNSrNWvN`zMezMezMezLezLezLezLfzKgzKgzKgzJfzJezJdzI\
dzIdzIdzIdzHdzGezFezEfzDfzDfzFgzGgzHgzIhzJhzKhzLhz\
NhzOdvPdrQdmRfhSieTleSjcRiaQg_PfYOdWNcUMaSL`QKZOJY\
MIWKHVIGTGFSEEQCEPAVEbUGaTH`SI_RKZRLYQMXPNWOPVOQUN\
RTMSSLURKVQKWPJXOIZNH_MH`LGaKFcJEdIDeHDfGChFBiEAjD\
AkDCjEDiFFhGGhHIgIJfILeJMeKNdLPcMQbMSbNTaOV`PW_QX_\
QZZR_YSaXTbXUdWVeVVgUWjrW }
frm:SliceJulibrot2 {; draws most 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),
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=sqr(z)+c
|z| <= 9 }
END PARAMETER FILE=========================================
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times.
