|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: Today's image makes use of a formula revised by Gilles Nadeau and posted to the Fractint list on Friday. (I have changed the space between Neo and T-set in the formula name to an underscore. A space band in a formula name is not permitted.) The formula is designed to draw the three-dimensional triternion Mandelbrot set. It does this very well. But I notice that the images it draws are the same as those drawn by the type=quat formula in Fractint, which claims to draw slices of a four-dimensional quaternion M-set, but which I have always suspected actually draws slices of a circular three-dimensional object. It is apparent that the three-dimensional object being sliced by both formulas is the figure that is traced out when the M-set is rotated around its X-axis. The value I gave (p1) in today's image is +0.64952, which is the Y-value of the prominent valley of the large north bud of the M-set. And not surprisingly, the valley appears in distorted form in today's image. The large open areas at the top and bottom of the frame are oblique slices of the northern bud itself, or rather of the donut-shaped ring this bud traces out as it rotates around the X-axis. The chaos across the middle of the frame is the fringe of the detail on the main-bay side of the valley, grossly stretched as would be expected when slicing through the edge of a donut. What I would like to see is a way of rotating the slice 90 degrees, so that the circles of revolution are drawn, and also the fascinating ovals that must lie in between. I have no idea of how to do this however. The image is titled "Triternion Travels", which is a fair enough opinion of the scene. Since the image has mathematical value but little artistic worth, I gave it no rating. The render time of 7-1/2 minutes on my 10-year-old machine may be avoided by visiting the FOTD web site at: A cloudy cool day here at Fractal Central on Friday went unnoticed by the dynamic duo of fractal fans, who still were more interested in playing with each other and waiting for another mouse to come out. They exhausted themselves playing, and showed little disappointment when no mouse appeared. The usual evening treat was fully enjoyed. My day was totally average. Tomorrow will probably be the same. Until then, when the next FOTD will shine forth, take care, and would the true number of dimensions that make up sub-atomic reality please stand up. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Triternion_Travels { ; time=0:07:26.44--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=Neo_T-set params=0.64952/0 maxiter=5000
center-mag=-0.124889193/0/42.27946/3.2951 float=y
inside=0 logmap=186 symmetry=xaxis periodicity=10
colors=000kdff_g`ViWQjTJmSKlRLkRMkQNjQNjPOiOPhOQhN\
RgNRgMSfLTeLUeKVdBjCGbRKVdJKuMMsONrQOqSPpUQoXRnZSm\
`TlbVjdWigXhiYgkZfm_eo`dtddqaco_cmYckWciUcgSceQccO\
caMc_KcYIcWGcUEcSCcN5fQAcSFaVK_XPYZTWaYUcbSfgQhlOj\
pMhqPfrSdrVbsX`s_ZtbXueWugUvjSvmQwpOxrMxuKyxJyzHwy\
FuxDsxBqwAow8mv6kv4iu3hu7isBjrFkpJloNmmRnlVokZpibq\
hfrfjsentcrubvx`uuatsasqasoarmaqkapiaqfbpgapgaph`p\
h`pi_oi_ojZojZokYokYnlXnlXnmWnmWnnVqoUnnVknVhnWenW\
cnW`nXYnXVnXSnYQnYNnYKnZHnZ4bsCsWFnZIj`LfbOaeRYgUU\
iXPl_LnbHpeCsh8uk4wn0yh9lcI_ZRNRX4TY8UZBVZEW_IY`LZ\
`O_aS`aVbbYccadcdedghghfdjdbkc_laYm_WnZToXRqWOrUMs\
SKtRHuPFvODwUEjZFZcGNMAELEGKHIKKJJNLJQMITOHWPHZRGa\
SGdUFgVEjXEmYDp_AxfCucDs`EqZGnWHlUIjRJhPPeUVcZ_abe\
_gkYlpWprVsAao8Wg7Q`6KU5EN7LK9RIBYGDcEFjCGpAAsU5ul\
`FLRMJHTI8ZHQaVgdhyfuvXotOirFcp6YmHWkRVh`TfjSdtR`m\
SXfST_TPTTLMUIFUFP`CZfAgm }
frm:Neo_T-set { ; Russell Walsmith
X=real(pixel), Y=imag(pixel), V=real(p1)
x1 = y1 = v1 = 0:
x2 = x1^2-y1^2-v1^2 + X
y2 = 2*x1*y1 + Y
v2 = 2*x1*v1 + V
x1=x2, y1=y2, v1=v2
z = x1^2+y1^2+v1^2
z < 8 }
END PARAMETER FILE=========================================
|
times.
