F.O.T.N. (Fractal of the Night) 26 Feb 1998 (Mickey Mouse)

In tonight's fractal we find Dr. J fooling around again with Paul Derbyshire's formula. He has generalized it, Eqn 1, by making the constant 2 a parameter. Figure 1 shows what he calls Mickey Mouse, a two eared Mandelbrot set resulting from putting the constant to 3.

1)   z := e^z+c(z+p)^-2

Shooting off from the ears are two small 'normal' Mandelbrot midgets.

Figure 1.  Mickey Mouse.

Stay warm,
Jay

frm:Explode_M_pj { ; by Jay Hill, 1998
; after Paul Derbyshire
c=pixel, p=p1; p1 is a constant in the formula
z=0 ; steps of Jay's formula
z=.2*z+.8*(-p+exp((log(2*c)-z)/3))
z=.2*z+.8*(-p+exp((log(2*c)-z)/3))
z=.2*z+.8*(-p+exp((log(2*c)-z)/3))
z=.2*z+.8*(-p+exp((log(2*c)-z)/3))
z=.2*z+.8*(-p+exp((log(2*c)-z)/3))
z=.2*z+.8*(-p+exp((log(2*c)-z)/3))
z=.2*z+.8*(-p+exp((log(2*c)-z)/3))
z=.2*z+.8*(-p+exp((log(2*c)-z)/3))
z=.2*z+.8*(-p+exp((log(2*c)-z)/3))
z=.2*z+.8*(-p+exp((log(2*c)-z)/3))
z=.2*z+.8*(-p+exp((log(2*c)-z)/3))
z=.2*z+.8*(-p+exp((log(2*c)-z)/3))
z=.2*z+.8*(-p+exp((log(2*c)-z)/3))
z=.2*z+.8*(-p+exp((log(2*c)-z)/3))
:
z=exp(z)+c/sqr(z+p),
real(z)<=900000
}

mickey_mouse_00 { ; (C) Jay Hill 1998
; generalization of Paul Derbirshire formula
reset=1960 type=formula formulafile=explode.frm
formulaname=explode_m_pj passes=2 center-mag=-16.5058/0/0.04/1/-90
params=3/0 float=y maxiter=2560 inside=0 outside=summ
colors=KAcAwA<44>121000000<142>yy0zz0xx0<29>220000000<29>000
}