Tonight's picture came in on my FractoFax only moments ago. The trouble is I'm not sure if it is Dr. J playing with his lap top FractintoScope games again or if this some kind of shoot out in FractoSpace. I have not asked him if there are crimes in FractalSpace. But we do know there are accidents which cause at least some inconvenience. Since the formula is that of Paul Derbyshire, I can assume he is playing with his computer. But with Dr. J we can only guess.
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Figure 1. Dr. J in a Laser Duel.
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 Mandelbrot set for this equation.
Stay healthy,
Jay
frm:Explode_M_2j { ; by Jay Hill, 1998
; after Paul Derbyshire
c=pixel
z=0, log2c=log(2*c) ; eight steps of Jay's formula
z=.2*z+.8*(-2+exp((log2c-z)/3))
z=.2*z+.8*(-2+exp((log2c-z)/3))
z=.2*z+.8*(-2+exp((log2c-z)/3))
z=.2*z+.8*(-2+exp((log2c-z)/3))
z=.2*z+.8*(-2+exp((log2c-z)/3))
z=.2*z+.8*(-2+exp((log2c-z)/3))
z=.2*z+.8*(-2+exp((log2c-z)/3))
z=.2*z+.8*(-2+exp((log2c-z)/3))
; finish with one of Derbyshire's Newton steps
z2=z+2
s=sqr(z2)
t=z2*s
ez=exp(z)
func=t*ez-2*c
der=3*s*ez+t*ez
z=z-func/der
: ; Derbyshire's formula
z=exp(z)+c/sqr(z+2),
real(z)<=900000
}
Laser_Dual { ; by Jay Hill, 1998
; uses Paul Derbyshire formula
reset=1960 type=formula formulafile=explode.frm
formulaname=explode_m_2j center-mag=-40.257/-15.802/11.23227/1/-90
float=y maxiter=800 inside=bof61 periodicity=0
colors=000<4>200mU0310<6>620mU0720<2\
8>L70L70M70N70<29>uJ0wK0wK0<94>ww0ww\
0vv0<76>000KKK hertz=1200
savename=laserdul
}
