############################################################## Below is the parm file for calculating the near-rectangular shape that has the embedded fractal tree I referred to in my Sept 19, '06 post. It is a zoom into Jim Muth's Oct 7, '03 FotD (Original date Jan 6th, 1998, often erroneously given as Jan 1st, 1998.) Here is a description of the fractal from my Sept 19, '06 post:

In addition to the object's clearly being a gently-curving rectangle of a single color, it has another really astounding feature. It has an embedded fractal pattern, like a pattern on a rug. The pattern is of a fractal tree composed of narrow triangles branching at right angles to one another.

A version of this tree-like shape is included in Mandelbrot's "The Fractal Geometry of Nature." I'm not able to locate my copy right now as I have just moved also, but if memory serves, Mandelbrot's version was created by a substitution process similar to the ones used to create Hilbert curves and Koch snowflakes.

Does anyone else think that it is unusual that a particular fractal formed by a simple substitution process could also be created by a complex formula 'finding' it hidden at a very specific location and rotation in the four-dimensional Julibrot? <---<< You can calculate it at a lower resolution than 1600 x 1200 to keep it from taking 52 minutes -- as it did on my P400. - Hal Lane ######################### # hallane@earthlink.net # ######################### START PARAMETER-FORMULA FILE================================ Projective_PlaneC { ; Hal Lane Sep22,06 51:31 P400 1.6Kx1.2K ; Zoom into Jim Muth's Oct 7, '03 FotD, ; the 'rectangle'. Shows a tree-like ; branching pattern a la substitution ; fractals like Koch snowflake. ; reset=1960 type=formula formulafile=pastengo.par formulaname=multi20031 function=flip/ident/ident/flip passes=1 center-mag=-0.00020758063848563/-0.00003926828671266/90\ 6.3389 params=88/88/0.00022/0.0755/-1.74308/0 float=y maxiter=1800 bailout=25 inside=253 logmap=yes symmetry=none periodicity=10 sound=off colors=000QVZ<2>PXZPYZP_Z<3>PfZPgZPiZPjZPlZPnZRt_<3>PnZ\ PmZPkZ<3>NaZN_ZNYZMVZMTZ<9>KGZJEZJDZ<2>I9ZI8ZJ6a<14>I8S\ I8RI8Q<2>I8OI8NH9KH9IH9HH9IH9IH9HH9FH9FH9H<6>HACHACHAB<\ 2>HA9HA9JCB<2>OIGQJHRMJ<3>YXP__RabSbdUdgVejW<3>lmbnncoo\ eqnf<3>wshxuixwjyylyzm<3>zxjzwizvhzug<3>zshzshyrg<4>uod\ tocsnb<3>ol_mkZkjY<3>chVagV_gUYfTWfS<3>S`PRZOQXNPYN<3>L\ WKKVJJVIIUHHTGGUG<3>I_IJ`IJ`I<32>ZpQ_qR_qR<3>asSXrT<14>\ mtQntQptQ<2>stPttPvvJvuM<3>oqWmpZmqZ<3>moZnoZopZskZwzZz\ wZzwZ } frm:multi20031 {; Jim Muth, best=ifif, fiif, fifi, iffi a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994, z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p2, c=cos(b)*fn3(real(pixel))+cos(a)*fn4(imag(pixel))+p3: z=z^2.003+c, |z| <= 100 } END PARAMETER-FORMULA FILE=============================== ######################################################### -- No virus found in this outgoing message. Checked by AVG Free Edition. Version: 7.1.405 / Virus Database: 268.12.7/454 - Release Date: 9/21/06