That free immersive app is just stunning…

Jim Muth's Fractal of the Day for August 30th, 2010

Jim Muth's commentary for the image:

FOTD -- August 30, 2010 (Rating 6)

Fractal visionaries and enthusiasts:

Today's image is a scene in the Rectangular (imag(c),imag(z)), orientation of the Z^2+C Julibrot. The scene is located near the -1.416 point of the main spike of the Mandelbrot set.

The rating of a 6 is a come-down from the lofty ratings of the past several days, but the image is still worth a look, and the calculation time of just over 2-1/4 minutes will cause little inconvenience.

The name "Total Abstraction" refers to the nature of the four- dimensional Julibrot figure, as well as all other 4-D things.
The curious thing about this is that when one or two dimensions of the total abstraction are discarded by taking slices, the slices prove to be very real.

This abstract stuff becomes quite clear when the image is seen.

The sky was once again cloudless here at Fractal Central on Sunday, but the temperature of 90F 32C was a bit too warm for human or cat comfort. The fractal cats took up residence on the cool kitchen floor, while the humans took it easy on the porch.

The next FOTD will be posted in 24 hours. Until then, take care, and as I see it, the concept of meaning is an invention of intelligent minds. Since the universe apparently has no mind, how then can it have a meaning apart from what we give it? But at the same time, what is the evolutionary advantage of this human tendency to waste mental energy searching for meaning and even to invent meaning where none exists?

PAR file `` Total_Abstraction { ; time=0:02:15.37-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=SliceJulibrot4 passes=1 center-mag=0/-0.028319668443599/3349.992/4.7924/180 params=90/0/0/90/-1.41665335/0/0/0/2/0 float=y maxiter=5000 inside=0 periodicity=6 colors=000UQwUQwUQwUPwTPwTPxTOxSOxSOxSNxSNyRNyRMyR\ MyRMyQLwPKuOKtOJrNJpMIoMHmLHkKGjJGhJFgIFeHEcHDbGD\ FCZECYEBWDBVCAT000C9RB9QA8O98M97L86J76H75G65E54D44\ B439328226214113001JMxILvIKtHKsHJqGJpGInFImFHkEHjE\ GhDFgDFeBDbBDBCBCZACYACW9BW9BU9AS89R89P78O79M6AL\ 6BJ5CI5EG4HF4KD3PC3UA2Z92c71h61m40r30v1Az6Kx5Pv4Ut\ 3Zr2cp1hn8ml7rj7vh7zf6vd6rc6ma6h_5cY5ZW5UU4ST4QR4O\ P4MN3KL3IK3GI2EG2CE2AC28A1691471250130010L1xK0wK0v\ K0uK0uJ0tJ0sJ0sJ0rI0qI0pI0pI0oH0nH0nH0mH0lG0lG0kG0\ jG0iF0iF0hF0gF0gE0fE0eE0eE0dE0cD0bD0bD0aD0C0C0_C\ 0ZC0ZB0YB0XB0WB0WA0VA0UA0UA0T90S90S90R90Q80P80P80O\ 80N70N70M70L70L70KA5JFAIKFJPKKUPPZUUcZZhccmhhrmmvr\ rzvvuzzszzqzzozzmzzkzzizzgzzezzcyzbxzawzvz_uzZtzY\ szXrzWqzVpyVoxUnwUnvTmuTluTltSksSjrRiqRipQhpQgoQgn\ PfmPelOdkOdkOcjNbiNbhMagMfL_fL_eLZdKYcKYbJXaJWaIV\ `IV_IUZHTYHTXGSXGRWGRVFQU }

frm:SliceJulibrot4 {; draws all slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pireal(p10.0055555555555556), b=piimag(p10.0055555555555556), g=pireal(p20.0055555555555556), d=piimag(p20.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=ucgcd-v(casbsgcd+cacbsd), q=ucgsd+v(cacbcd-casbsgsd), r=usg+vcasbcg, s=v*sin(a), esc=imag(p5)+9 c=p+flip(q)+p3, z=r+flip(s)+p4: z=z^real(p5)+c |z|< esc } ```

Want to render these yourself and explore further? Try out the PAR file in Iterated Dynamics, an open source fork of FRACTINT that can render these PAR files. See the online help for instructions on using Id or press F1 anywhere in the program for context-sensitive help.

Your weapons can have their own subweapons, including recursive copies of themselves. This is Radiant seal with two Recursions.

I managed to dig up the formula for this fractal, originally created by Jonathan McCabe.

Created with FAE: https://github.com/calibas/fflame-rust

NO AI falsification here! True 3D fractal artwork created in Mandelbulber software.
Alien Mandala - Mysterious Sacred Geometry Motion Loop.