2017-01-19_r[-0_1]i[0]_1

My friend Jason / Softology rendered a deep zoom of this set and put it on YouTube, check it out!

www.youtube.com/watch?v=8Hci_vNr6sI

 

Aso check out his program Visions of Chaos: softology.com.au/voc.htm

 

((((z*z+c)*(z*z+c)+(c*c+z))*((z*z+c)*(z*z+c)+(c*c+z))+((c*c+z)*(c*c+z)+(z*z+c)))*(((z*z+c)*(z*z+c)+(c*c+z))*((z*z+c)*(z*z+c)+(c*c+z))+((c*c+z)*(c*c+z)+(z*z+c)))+(((c*c+z)*(c*c+z)+(z*z+c))*((c*c+z)*(c*c+z)+(z*z+c))+((z*z+c)*(z*z+c)+(c*c+z))))

 

Mandeljulia?

 

While this IS a Julia rendered formula colored according to Newton and Log(|Z|), it follows the rough pattern of the Mandelbrot fractal.

 

This makes sense, even though it does so for only ONE particular value of real, because the formula is itself a meta-Mandelbrot. Look at it. I simply followed the convention of z*z+c to three levels...so thing A times itself plus thing B. Thing B is simply an inverted thing A which follows the same convention.

 

Level 0 is:

z*z+c

 

Level 1 is:

((z*z+c)*(z*z+c)+(c*c+z))

 

Level 2 is:

(((z*z+c)*(z*z+c)+(c*c+z)) * ((z*z+c)*(z*z+c)+(c*c+z)) + ((c*c+z)*(c*c+z)+(z*z+c)))

 

Level 3 is the formula above.

 

Try this technique yourself with other models, you will get interesting results!

Done