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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image takes us to the tip of the negative spike of the Mandelbrot set, where we examine a tiny minibrot. In fact, it is the most remote minibrot on the spike reachable with conventional math. But where is the minibrot? Actually, it is very close. The problem is that we have perturbed the view, and therefore have just missed the minibrot. But we have come close enough to skim through the outer fringes of the pattern around it. To see the actual unperturbed minibrot simply reset the real and imaginary p2 parameters to zero and shift the view a bit. I have added to the interest by reducing the bailout radius, which is real(p4), to the point where the entire scene is on the verge of being swallowed up entirely. I have added even more interest by rendering the image with the outside set to 'tdis'. I named the image "Out on a Filament", since that is its location. But the rating of a 6 was all I could do for an image that is basically just another trip to the over-viewed negative spike of the Mandelbrot set. The calculation time of a sizzling 39 seconds will try the patience of no one. And the task of calculating the scene may be done away with entirely by going to the FOTD web site at: As I write this, I wonder what this Mandelbrot-set location would look like in some of the odd orientations through the Julibrot. Well, there is one way to find out, and that is to go and look. If I find anything of exceptional interest, it will appear as a future FOTD. The weather was too warm for comfort here at Fractal Central on Thursday, with a high temperature of 90F 32C and quite sticky humidity. In the evening however a light thunder-shower cooled things down a bit. The fractal cats don't worry themselves with outside heat unless there are squirrels to go along with it. If there are no squirrels, a chipmunk or two will do. My day was appropriately busy and tomorrow promises to be the same. The next FOTD is due in 24 hours. Until then, take care, and give particular attention to the questions that appear to have no answers. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Out_on_a_Filament { ; time=0:00:39.39-SF5 on P4-2000
reset=2004 type=formula formulafile=slices.frm
formulaname=MandelbrotVE-VP passes=1 periodicity=10
center-mag=-1.99999977939708600/-0.000000000000023\
21/2.706509e+013/1/2.47067461084123785/0 inside=0
float=y maxiter=3000 outside=tdis symmetry=none
params=2/0/1.3e-007/6e-008/0/0/1.9999997799/0
mathtolerance=0.05/1
colors=000wfapfZifW9x5PoH7phIlbTiYcbxcdmcebbJncVcQ\
kbViZ_gWVPFYVK``PVrUYnT`jTC4SKaXUdVeJ1dRBcZKQ5LXOP\
JJjU_bUSiXWdZ_`acXRPrmceGG2MR9S`GYaNO3LWNPzr2zhBzU\
KLEQQMRVTS__TNLRSRSWWS_aTcz7arFblMOK1SQ8WWF_aM_Uz`\
Yza`HbcNTeWWfVZfUafz_EzWcz_fzpGzkPzgYzSHzWQNUdzdSz\
oFzy3wwMlvdbuwToqXikzcfzeadgXziShgWdGprf_`dczb8zcH\
BcQHcZNH9wTQgoTzkYigb`eDxrHtnOmjUff`_W5cZI_aVzu2ho\
GbiUY3rGMlNLM`6`KoNziXKWk1Yi8_hFagMFRjSZzK1GRFLYTP\
1j8BiELhJVgOStVVpUYmU`iTHBHTRN9fvPfgQGHVPL_YPtQcVB\
HYML`XP86095pHFjPOdXYZOt19KuHY8TbJ_v`qndlk`ghXbBGc\
MLcXPsEuoMmkTfg__4McGT_S_WUmtYjj`haIRCQXIXaOWpfYmb\
_k_ahWwBNpMPiXR`6JaGMbPOcYRL9JSLNYWQhoSflTejTdhTHs\
HNoKTlNZiQVzZYsX`lVhGgeU_2ljFjdShZptolpiimcfiYR0FY\
MMwowplliibqpVllUgiTt3NoDPkNQgXSMUp5XuD4tMHjVUaCw1\
MqBVkKtlWkiUUxcXs`ZoYajVjmJgjNehQhHVeUU9j0Hi8PhFXg\
Mi2EWz7cGzd8ZcQWZNi`Ucb`Y }
frm:MandelbrotVE-VP {; Jim Muth real(c),imag(c)
a=p1, z=p2, c=pixel+p3,
b=sqr(real(p4)):
z=z^(a)+c,
|z| < b }
END PARAMETER FILE=========================================
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times.
