| May 9, 2011: A Hidden Peninsula | May 7 | May 10 | 2011 | FOTD Home |
Fractal
visionaries
and enthusiasts:
Today's image takes
us to the land of the mysterious Z^(2.003)+C Julia rectangles.
But today we are not concerned with Julia rectangles. Today we
are after bigger game. We investigate the Mandelbrot aspect of
the area.
In the Mandelbrot orientation, the Julia rectangle corresponds to a
tiny peninsula jutting west into a tiny bay on the east shore line of
the strait connecting the partially overlapping large minibrots on the
infinitely divided main spike of the Z^(2.003)+C Mandeloid.
When I first arrived in this Mandelbrot area, I almost gave up.
Nothing even remotely resembling a rectangle or a minibrot was
visible. But after a short search I stumbled upon a feature with
the 2-way symmetry that often indicates the presence of a
minibrot. Today's image shows the minibrot that I found.
Since Mandelbrot sets are kind of catalogs of all the Julia sets
created by a particular formula, today's image should be filled with
open rectangles, and indeed they are there, most of them beyond
resolution but some well within range. In tomorrow's FOTD a
full-blown Mandelbrot rectangle will be featured.
The name "A Hidden Peninsula" refers to the tiny peninsula that holds
today's scene. The rating of a 7 is FOTD average.
BTW, we are considering posting a picture gallery of the cat action
here at FOTD. I have been writing of the fractal cats for
many years. Now we feel it is about time to give them the
exposure they deserve.Today's image takes us to the land of the
mysterious Z^(2.003)+C Julia rectangles. But today we are not
concerned with Julia rectangles. Today we are after bigger
game. We investigate the Mandelbrot aspect of the area.
In the Mandelbrot orientation, the Julia rectangle corresponds to a
tiny peninsula jutting west into a tiny bay on the east shore line of
the strait connecting the partially overlapping large minibrots on the
infinitely divided main spike of the Z^(2.003)+C Mandeloid.
When I first arrived in this Mandelbrot area, I almost gave up.
Nothing even remotely resembling a rectangle or a minibrot was
visible. But after a short search I stumbled upon a feature with
the 2-way symmetry that often indicates the presence of a
minibrot. Today's image shows the minibrot that I found.
Since Mandelbrot sets are kind of catalogs of all the Julia sets
created by a particular formula, today's image should be filled with
open rectangles, and indeed they are there, most of them beyond
resolution but some well within range. In tomorrow's FOTD a
full-blown Mandelbrot rectangle will be featured.
The name "A Hidden Peninsula" refers to the tiny peninsula that holds
today's scene. The rating of a 7 is FOTD average.
BTW, we are considering posting a picture gallery of the cat action
here at FOTD. I have been writing of the fractal cats for
many years. Now we feel it is about time to give them the
exposure they deserve.
Saturday brought clouds and rain showers to Fractal Central, while
Sunday brought lots of sun and a temperature of 68F 20C, earning the
approval of the fractal cats. On the human side of things,
nothing went wrong, which makes for a satisfactory day.
The next FOTD will be posted in 24 hours. Until then, take care,
and before you put your faith in skepticism, think rationally about it.
Jim Muth
jamth@mindspring.com
START PARAMETER FILE=======================================
A_Hidden_Peninsula { ; time=0:06:32.48-SF5 on P4-2000
reset=2004 type=formula formulafile=slices.frm
formulaname=MandelbrotN center-mag=-1.743496834151\
223/+0.00000003977466762/1.077858e+011/1/22.5/0
params=2.003/0/0/0/0/0 float=y maxiter=7500
passes=1 inside=0 logmap=854 periodicity=6
colors=00005U04P03K02F57FCB8JF6QJ4XN2bR0lOTvMtnQqf\
UoZYlRajJegBie3lcKraOnXRkSVgNYdIVcMScPQcSNcWLcZIca\
GcdLWnNYiP_dR`_SbVUdQWeLYgGZhCOQOSTTWWX_Z`cadgdhjg\
loUfsG`w3Vr7VnBVjFVfIVbMVZQVVTVhfRutOsrSqqWooZmnbk\
lfikigimfhpg`WhUCb_AXd9Ri8Ln7Fs6Ax5TtOjpfblbWi_PeX\
IbUBZR4WOARQFNSLJUQFWWBY`7_e3ag7_hBYjEXkIVmLUnPSoS\
Rc_XTgaHof6vkDwlKxlRymYzmczm0iW7jZDk`KlcQleXmhbnji\
omooonihncbnYXnTQnNKnHEnC8kG9iJAfMBdQCaTD_WDtTcfJQ\
TACLFDDJE6NFBKHFIIJGJODKSBLW9MTJQQTUOaXUeRZiMdmHiq\
Bou6ty1oo4jf6fY9aPBYGDWFFUFHSFJQELOENMEPLERJFRHGRA\
0KPMOYSMgXJpbHygFwYPuPZsGhr7qjCscGtXKuQPwJTxCXy5`z\
CazIblPcfKPU`eTgfNmgGsgAlj8el7Zn5Tp4Mr2Fz1Uz0PcAcM\
Kr4TqOapgiozqnremkVmdKoeIpgHriFsjEulCvmBxo9yp8wqDv\
qHtqLsrPrrUprYosamselsjktnitrhtvgtzftyetydtxctxctx\
btwatw`tv_tv_tzYszWszUrzSrzczzczzczzmzzmzzmzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
frm:MandelbrotN {; Jim Muth
b=p1, z=p2, c=p3+pixel:
z=z^(b)+c,
|z| <= 16 }
END PARAMETER FILE=========================================
Saturday brought clouds and rain showers to Fractal Central, while
Sunday brought lots of sun and a temperature of 68F 20C, earning the
approval of the fractal cats. On the human side of things,
nothing went wrong, which makes for a satisfactory day.
The next FOTD will be posted in 24 hours. Until then, take care,
and before you put your faith in skepticism, think rationally about it.
Jim Muth
jamth@mindspring.com
START PARAMETER FILE=======================================
A_Hidden_Peninsula { ; time=0:06:32.48-SF5 on P4-2000
reset=2004 type=formula formulafile=slices.frm
formulaname=MandelbrotN center-mag=-1.743496834151\
223/+0.00000003977466762/1.077858e+011/1/22.5/0
params=2.003/0/0/0/0/0 float=y maxiter=7500
passes=1 inside=0 logmap=854 periodicity=6
colors=00005U04P03K02F57FCB8JF6QJ4XN2bR0lOTvMtnQqf\
UoZYlRajJegBie3lcKraOnXRkSVgNYdIVcMScPQcSNcWLcZIca\
GcdLWnNYiP_dR`_SbVUdQWeLYgGZhCOQOSTTWWX_Z`cadgdhjg\
loUfsG`w3Vr7VnBVjFVfIVbMVZQVVTVhfRutOsrSqqWooZmnbk\
lfikigimfhpg`WhUCb_AXd9Ri8Ln7Fs6Ax5TtOjpfblbWi_PeX\
IbUBZR4WOARQFNSLJUQFWWBY`7_e3ag7_hBYjEXkIVmLUnPSoS\
Rc_XTgaHof6vkDwlKxlRymYzmczm0iW7jZDk`KlcQleXmhbnji\
omooonihncbnYXnTQnNKnHEnC8kG9iJAfMBdQCaTD_WDtTcfJQ\
TACLFDDJE6NFBKHFIIJGJODKSBLW9MTJQQTUOaXUeRZiMdmHiq\
Bou6ty1oo4jf6fY9aPBYGDWFFUFHSFJQELOENMEPLERJFRHGRA\
0KPMOYSMgXJpbHygFwYPuPZsGhr7qjCscGtXKuQPwJTxCXy5`z\
CazIblPcfKPU`eTgfNmgGsgAlj8el7Zn5Tp4Mr2Fz1Uz0PcAcM\
Kr4TqOapgiozqnremkVmdKoeIpgHriFsjEulCvmBxo9yp8wqDv\
qHtqLsrPrrUprYosamselsjktnitrhtvgtzftyetydtxctxctx\
btwatw`tv_tv_tzYszWszUrzSrzczzczzczzmzzmzzmzzzzzzz\
zzzzzzzzzzzzzzzzzzzzzzzzz }
frm:MandelbrotN {; Jim Muth
b=p1, z=p2, c=p3+pixel:
z=z^(b)+c,
|z| <= 16 }
END PARAMETER FILE=========================================