F.O.T.N. (Fractal of the Night) 25 Jan 1998 (FractoBowl)

Dr. J had been watching the FractoVision pre-game activity from his hospital bed. You know, it is amazing how fast one can recover from an injury when properly motivated. Dr. J has left the hospital and headed for the FractoBowl. After stopping by the ATM and withdrawing the maximum, he has obtained a very pricey ticket from a scalper. I didn't ask how much it was this time. The view of the FractoBowl, taken from somewhere in one of those other dimensions, is very beautiful. Alas, I can supply only a 2D reproduction. In tonight's image, kindly forwarded to us from an undisclosed location somewhere in Fractal land, shows lush parkland surrounded by the beaches and ocean. By the way, I also did not ask how he got the image, nor that of last night's Fractoball. If you look closely, you can see the fans have already gathered in the Bowl, with more streaming in from all sides. The orange on the left and the yellow on the right.

Figure 1. FractoBowl

You can get your 3D glasses, two sets, along with 27 striking astronomical images in the March 1998 issue of Astronomy magazine. So aim your Car-dioid toward your nearest magazine rack. Future FotN pictures may be in 3D. But for tonight, we shall have just shading effects.

Tonight's picture shows some Fractint technology that I have been wishing to try for some years. Until now, I have settled for Borland C++ images with the usual limitations of home brew code. Many thanks to Rich Thomson, Kerry Mitchell, Paul Carlson, Sylvie Gallet , Damien Jones, Lee Skinner, Paul Derbyshire and many more on the Fractint list for sharing their formulae.

Here are the Fractint parameter files, in which I am quite pleased!. Tonight's formula uses the

z := z³ + c

family of the Mandelbrot sets. The derivative with respect to c is used to control lighting. The derivative gives us the rate of change of the final z iterate as a function of c, the picture coordinate. So, if the magnitude of z is increasing as pixel position is moved toward the light, we color it with lighter colors.

Enjoy your FractoBowl Game. Hope you get a good seat!
Jay

frm:Colorit-3 { ; (c) Jay Hill, 1998 b=p1 ; p1=cos(a)+i*sin(a), a=light angle if(p1==0) p1=1 endif done = 1, iter=0, z = 0, zc = 0, c = pixel, dz=1: a=pi*p1/180, b=cos(a)+i*sin(a) ; p1= light angle (deg) done = 1, iter=0, z = 0, zc = 0, c = pixel, dz=1 : ; initialization. iter = iter+1 ; gotta count em dz=3*sqr(zc)*dz+1 ; derivative, dz/dc zc=zc*sqr(zc) + c ; standard MSet iteration if(|zc| >= 1024) ; Bailout z = z -8 + ((sin(2*pi*iter/256)*Real(b*dz/zc))>0) + iter done=-1 ; Set flag to force an exit. endif done >= 0 ; Continue if the flag >=0. }

FractoBowl { ; (c) Jay Hill, 1998 FractoBowl reset=1960 type=formula formulaname=colorit-3 center-mag=-0.306369/0.967432/42.24249/1/-55 float=y maxiter=2560 inside=0 outside=real periodicity=0 colors=UmAVTTxvtVTTxvuUUUwwwKKKmmmUUU0Ac08w0Ed0Hw0Ie0Pw0Mg0Yw0Rh0ew0Vj0n\ w0ZkwmUcSH0mK0U02mJ1U05nI3U07nH5V0AoG6V0CoF8W0FpDAW0IqCCX0KqBDX0NrAFX0Pr\ 9HY0Ss8JY0Vt6KZ0Xt5MZ0wK0mc0wK0mc0wK0mc0wK0mc0wL0mc1wL1mc1wL1lc1wM1lc1wM\ 1lb2wM1lb2wN2lb2wN2kb2wN2kb3wO2kb3wO3kb3wO3kb3wP3ja4wP3ja4wP3ja4wQ4ja4wQ\ 4ja5wQ4ia5wR4ia5wR4ia5wR5i`6wR5i`6wS5h`6wS5h`7wS6h`7wT6h`7wT6h`7wT6g_8wU\ 6g_8wU7g_8wU7g_8xV7g_9xV7f_9xV8f_9xW8f_9xW8fZAxW8fZAxX8eZAxX9eZAxX9eZBxY\ 9eZBxY9eZBxY9dZBxYAdYCxZAdYCxZAdYCxZAdYDx_BdYDx_BcYDx_BcYDx`BcXEx`BcXEx`\ CcXExaCbXExaCbXFxaCbXFxbDbXFxbDbXFxbDaWGxcDaWGxcDaWGxcEaWGxdEaWHxdE`WHxd\ E`WHyeF`WHyfG`VIyfH`VIygJ_VIygK_VJyhL_VJyhM_VJyiO_VJyiPZUKyjQZUKyjSZUKyk\ TZUKxkUZULxlVYULxlXYULxmYYULxmZYTMxn`YTMxnaXTMxobXTMxocXTNxpeXTNxpfXTNxq\ gWSOxqhWSPxrjWSPxrkWSQxslWSQxsnVTRxtoVTRxtpVTSxuqVTSxus }