Tonight's picture came in on my FractoFax in reply to repeated requests about how he is. Some of us are worried about what was going on in last night's picture. The picture was troubling, since I'm not sure if it was Dr. J playing with his lap top FractintoScope games again or if it was some kind of shoot out in FractoSpace. Indeed, the equation was Paul Derbyshire's and Dr. J was playing with his computer again. And guess what, he won this time. Figure 1 shows us the picture that came up on his screen when he won. It is a Julia set corresponding to a point near the base of the 3-bud in the equation's corresponding Mandelbrot set. That explains the three way (near) symmetry.
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Figure 1. Dr. J Wins One.
A little math. Paul Derbyshire offered a Mandelbrot set form of the following iteration formula.
1) z := ez+c(z+2)-2
The frm file creates a Julia set for this equation.
Stay healthy,
Jay
frm:Explode_J_2j { ; by Jay Hill, 1998
; after Paul Derbyshire
c=P1 ; p1 is the Julia parameter
z=pixel
: ; Derbyshire's formula
z=exp(z)+c/sqr(z+2),
real(z)<=900000
}
PuzzleJ3 { ; by Jay Hill, 1998
; based on Paul Derbyshire formula
reset=1960 type=formula formulafile=explode.frm
formulaname=explode_j_2j center-mag=0.103869/1.67193/2.140346
params=-3.6662/2.4134 float=y maxiter=900 inside=bof61 periodicity=0
colors=000111w335w577w999<9>ccc<14>L\
LLJJJKKK<19>uuuwwwwww<40>hhhhhhhhhhh\
hhhh<31>cppKjj0ccc0ccc0iiJoob<4>ssqtttsss<110>000
savename=puzzlej3
}
