April 1, 2013: A Rectangular Set | March 31 | April 3 | 2013 | FOTD Home |
Fractal visionaries and enthusiasts:
Today's
image is a
new view of a minibrot hole on the main stem of the Mandelbrot
set. The minibrot looks so unusual because it is sliced in
the
Rectangular orientation, which lies at a right angle to the Mandelbrot
orientation and is determined by the imag(z) and imag(c) axes.
The brilliant green bars slicing diagonally through the open area are
actually Mandelbrot valleys viewed at a right angle. The bars
are
straight edged because regardless of where points in the M-set are
initialized, they will eventually settle into the same orbits unless
they escape first.
There is no way I could give a rating to such an overworked theme, but
being fascinated by things beyond visualization, I continue returning
to the four-dimensional Julibrot for ever new surprises.
The name "A Rectangular Set" is a bit misleading. The image
is
merely a small part of one of an infinity of Rectangular sets.
The calculation completes in 25 seconds, fast enough to waste no one's
time. The web sites are more convenient but probably no
faster.
The day began pleasant enough here at Fractal Central today, with
breaking clouds and a temperature of 50F 10C, but by midday the clouds
and rain had returned, and the temperature had dropped to 45F
+7C. The fractal cat observed all this with dis-interest,
while
the humans made it through another day with no unexpected disasters
happening.
The next FOTD will be posted soon. Until we find out how long
'soon' is, take care, and when disasters happen, look to the bright
side. But before you look, be sure a bright side actually
exists.
Jim Muth
jimmuth@earthlink.net
START PARAMETER FILE=======================================
A_Rectangular_Set { ; time=0:00:25.00 SF5 at 2000MHZ
reset=2004 type=formula formulafile=basicer.frm
formulaname=SliceJulibrot4 center-mag=0/0/10166.07\
/1.3984/29.6185420924715608/28.9858769262522351
params=90/90/0/90/-1.690128/0/-1.690128/0/2/0
float=y maxiter=3200 inside=0
logmap=28 periodicity=6
colors=000BamCalD`kE_jFZiGYgHXeIWcJVaIU_ISYHQVHOSG\
MQGKNFIKFGIDDGBADA89846713940B72E94HC6KF8OHARKCUME\
YPG_SGbUFdXEf_DiaCkdBmfAlgClhDkiEkjFjkHjlIilJimKhn\
LhoNgpOgqPfrQfrRhoUjmXlk_nibpgerehtckvanx_qqXlkUgd\
RbZOYSLTMIONJJOLPWSUpfGoaHnYHmTHlPHkLHgNIcOI_PIWRJ\
SSJPTJSPGVMEYIC`FAaJDaNGbRJbVMcYOcaRdeUdiXem_epadm\
bdjbdgbLTRLUQKVQKWQJXPJYPIYPIZPH_OH`OGaOGbNGcNFcNF\
dMEeMEfMDgMDhLCiLCiLBjKBkKBlKAmJAnJ9oJ9oJ8pI8qI7rI\
7sH6tH6uH6uH7tI7sI8sJ8rJ9rK9qK9qLApLApMBoMBnNBnNCm\
OCmODlPDlPDkQEkQEjRFjRFiSFhSGhTGgTHgUHfUHfVIeVIeWJ\
dWJdXJcXKbYKbYLaZLaZM`_M`_M_`N_`iSVgTVeTVdTVbUV`UV\
_VVYVVWVVVWUTWURWUQXUOXUMYULYUJYUHZUGZUE_UC_UB_U9`\
U7`U6`U7aT8bT9bT9cTAcSBdSCdSCeSDfSEfRFgRFgRGhRHhQI\
iQIjQJjQKkQLkPLlPMlPNmPNmPOnOPoOQoOQpORpNSqNTqNTrN\
UsNVsMWtMWtMXuMYuLZvLZwL_wL`xLaxKayKbyKczKczKbxLaw\
L`vM`uM_tNZsNYrNYqOXpOWoP }
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=========================================