; June 23, 1997: Offside Penalty ; ; offside ; ; Fractal visionaries: ; ; Fractals are almost magical in the way they can create so much beauty ; from so little information. How is it possible that a formula as simple ; as Z^2+C can hold within itself the infinity of information contained in ; the Mandelbrot set? Are mystical forces actually involved? ; ; The answer, of course, is that the formula is not the carrier of the ; infinitely detailed Mandelbrot set, but merely a set of directions ; telling us which way to go to build the set and reveal for ourselves the ; potential riches that are always waiting there. ; ; The Mandelbrot set never runs out of surprises. It is part of a larger ; object, the four-dimensional Julibrot figure, which I am currently ; exploring. Just as the Mandelbrot sets and the Julia sets each have ; their distinctive, easily recognizable characteristics, as well as their ; similarities, the XZ, XW, YZ, and YW sets each have their own ; distinctive characteristics as well as their similarities. ; ; Today, and every day for the rest of this week, I will concentrate on ; the YZ direction by posting images sliced in that direction. Then I'll ; devote a week to images from each of the other three slices. This does ; not imply, however, that the quality of the images will be compromised. ; The other slices are every bit as rich as the Julia and Mandelbrot ; slices. ; ; Today's fractal is a picture of a midget -- not a Mandelbrot midget, nor ; a Julia midget, but a YZ midget. The midgets in this plane have ; characteristics a bit closer to the Julia plane than the Mandelbrot ; plane, though not close enough to be mistaken for a Julia set. The ; feeling of great forces at work stretching the shapes like cosmic ; rubber, so evident in today's fractal, is a feature that characterizes ; the entire YZ world. ; ; The finished image has been hopefully posted to a.b.p.f. and a.f.p. I ; say hopefully because I've had a couple images vanish recently. ; ; Jim Muth ; jamth@mindspring.com ; ; START 19.6 COMBINED FILE=================================== Offside_Penalty { ; time=0:01:13.60-SF5 on P4-2000 reset=1960 type=formula formulafile=basicer.frm formulaname=Man2-YZ passes=1 center-mag=+0.2750977\ 599871218/+0.0027705419458246/102.6103/1.0402/\ 7.80896713033748036/-0.605979584844571262 params=-0.003/-1.748 float=y maxiter=7200 inside=0 logmap=yes periodicity=10 colors=000U3jV4iV4hW5fX6eX6dY7cZ8aZ8`_9_XCZVGXSJWP\ MUNQTKTRIXQF_OCbNAfL7iK7kJ7mI8pI8rH8tG8vF8rG9nH9jI\ 9fJAbKAZLAUMBQNBMOBIPCEQCARMNOW`LemIozFkqFghFc_FZS\ FVJFRAFN1FM5FL9FKDFJHEILEHPEGTEGWEF_EEcEDgECkDBoDA\ sD9wDBtHDrMFoQHmUJjZLhbNegPckR`oTZtVWxzRQjRUVQYFQa\ GTZGWWHZUIaRJdOJgLKjILmGLpDMsAMu8LrBLpDLmFLkHLhJLf\ LLcNLaPLZRLXTLUVcgfafe_ddZccXbbVaaT__RZZQYYOWXMVW6\ Ly8MvANrBOoDPkFQhHRdISaKTYEiuEhtFgrFgqFfpGezGdzGcz\ HczHbzIazI`zI_zJ_zJZzJYzKXzKWzKWzLVzLUzwAzoEzgIz_M\ zSQzVNzUOzUOzTPzSPzRQzRQzQRzPRzPSzOSzNTzMTzMUzLUzZ\ FzYGzXIzVJzUKzTLzSNzROzQPzOQzNSzMTzaRz`Rz_RzZRzYSz\ YSzXSzWSzVSzUSzTTzSTzRTzQTzPTzPTzOUzNUzMUzLUzgAzeB\ zdDzbEzaFz_HzZIzXKzVLzUMzSOzRPzPQzOSzMTzN2zN4zN7zM\ 9zMBzMEzMGzMJzMLzLNzLQzLSzbGzaHz`Iz_JzZKzYKzXLzWMz\ VNzTOzSPzRQzQRzPRzOSzNTzMUzqXzoXzmXzkWzjWzhWzfWzdW\ zbVz`VzZVzXVzWVzUUzSUzQUz } frm:Man2-YZ { z=real(pixel)+flip(real(p1)), c=flip(imag(pixel))+imag(p1): z=sqr(z)+c, |z| <= 36 } ; END COMBINED FILE========================================== ;