; May 28, 1997: Nowhere in a Hurry ; ; nowhere ; ; Fractal visionaries: ; ; No other fractal is quite like the Mandelbrot set. No other fractal ; gives so great a variety from so simple a formula. But the Mandelbrot ; set is but one in an endless series of similar fractals. There is no ; reason one must stop at Z^2+C; the formula works just as well with ; Z^3+C, Z^4+C, or Z^n+C. ; ; However the higher order mandeloids soon degenerate into a monotonous ; circle with n-1 identical bays. Indeed, when n is greater than 12, the ; sets are barely distinguishable from one another, and the midgets, which ; grow in size and number until they nearly obliterate all else, soon ; become uninteresting off-center circles. The only really interesting ; higher order Mandeloids are the Z^3, the Z^4, and to some extent the Z^5. ; ; Today's fractal, all_nine, is a symmetrical order 3 midget that I picked ; in honor of the Z^3 mandeloid, which gets far less attention than it ; deserves. The midget is located on the negative x-axis of its parent ; fractal. I realize that the order 3 mandeloid doesn't normally have ; midgets on its negative tail, in fact it doesn't have a negative tail at ; all. But I cheated a bit by writing a formula that gives it one, ; complete with midgets. ; ; The little two-headed midget sits surrounded by its pattern, glowing ; like a vision of the holy grail, with its arms radiating around it in ; ascending powers of three, rather than in powers of two. Thus instead ; of 4, 8, 16, we have 9, 27, 81. BTW, this same ; increasing-powers-of-the-exponent sequence continues into the higher ; orders, though the features soon become too tiny to be distinguished. ; The sequence also prevails in the fractional order mandeloids, which is ; why those figures must be filled with such annoying discontinuities. ; ; Jim Muth ; jamth@mindspring.com ; ; START PARAMETER-FORMULA FILE FOR 19.6============================= Nowhere_in_a_Hurry { ; time=0:00:39.87-SF5 on P4-2000 reset=1960 type=formula formulafile=basicer.frm formulaname=Mytest02 passes=t center-mag=-1.75424934433985100/0/2.054466e+011 params=1/0/1/0/3/0 float=y maxiter=1500 inside=0 logmap=yes symmetry=xaxis periodicity=10 colors=000`R`XTcTVfPYiK_lGaoCcrswHrtKprMooPmlRliUj\ gWidZga`YdWOgRDjL3mGAgKIbPPXTWSYbMajHfqBjrEgrIcsL`\ tOXtRUuVQuYNv`JWUETPCQLBNG9KC8H76IAFJDOKGXLKfMMdNP\ aOSZPVXQYUR`RScOTfLSfQRfVPe_OedNdiLdnKcsJaqH_nGZlE\ XiDVgCTeARb9Q`7OY6MW4KT5OX6T`7Ye8bi9gmAlrBqvCftDVr\ FJoEIlDGhBFeADb9CZ8AW69S57PCFPJNOccGcbGcbGcaGbaGb`\ Gb`Gb_GbZGbZGaYGaYGaXGaXGaWFaVFaVF`UF`UF`TF`SF`SF`\ RF_RF_QF_QF_PF_PF_OG_OFAdkBdjBcjCciDbhDbgEagEafF`e\ G`dG`cG`bG`aG`_HaZHaXHaWHaUIbSKbTNbUPbVScWVcYYcZ_c\ _bd`edagdbjdcmdepefreguehodehdbbc`WbYQbVJaSC0PD0OF\ 0NG0MH0LI0KK0JL0IM0GP0FR0EQ0DS0CT0BV09W08X7GY6OZ5X\ _4d`3ma2ud8ufEtiLtkRsnXspbrsiruoqxuqsldobRjUEaOGSI\ JJDL97O01Q21P41O61N81M91LB1KD1JF1IH1HJ1GI2IH4LG5OF\ 7RE9UDAXCC_AEb7N`3Wi7eiCerHeqLeqQepUeoZexcezhezlez\ qezpbzn_zmXzkUziWzhYzf_zeazccza`za_zbczbbzcazdezdd\ zeczegzffzgizaozWvzQzzZzz } frm:Mytest02 {; Jim Muth z=c=pixel: z=((z*(z+p1))^p2)^p3+c, |z|<100 } ; END PARAMETER-FORMULA FILE FOR 19.6=============================== ;