They Found It, The Master Code That Governs Everything | Gregg Braden

how to contain an infinite amount of space and time in a finite mass Z=Z*2+C

Z1 = Z^2 + C where Z1 = what you got for Z^2 + C

Then Z2 = (Z1)^2 + C and Z3 = (Z2)^2 + C etc.

Z is the independent variable, C is a constant.

z and c are complex numbers.  c is a constant:  a coordinate somewhere within two units of the origin.  The Mandelbrot set is constructed by taking a point from this area and repeatedly applying the formula zn+1=z2n+c until the result heads off to infinity.  The value of n is used to select the color of the pixel represented by that point.

I believe z0=0+0i.

both z and c are complex numbers.

Let's change this to real numbers instead.

We use:

z=x+iy

Where x,y are your usual coordinates in the Cartesian plane.

We also need:

i⋅i=−1

We have:

z2=(x+iy)(x+iy)=x2+2ixy+i2y=(x2−y2)+i(2xy)

We also need:

c=cx+icy

If we use these two expressions and substitute in:

zn+1=z2n+c

We get:

zn+1=xn+1+iyn+1=(x2n−y2n+cx)+i(2xnyn+cy)

Or:

xn+1yn+1=x2n−y2n+cx=2xnyn+cy(1)

If you want to graph this follow the following procedure:

Use initial values:

x0=0,y0=0

For every point (cx,cy) on the ‘screen':

cxcy∈∈[−2.5,1.5][−1.5,1.5]

Iterate expression (1) a fixed number of times (say 256 times).

If xn,yn escapes at a certain iterate k:

x2k+y2k>4

Colour the point (cx,cy) with ‘colour k'.

If xn,yn have not escaped after these 256 iterates, declare this point cx,cy to be inside the Mandelbrot-set. And give it a special colour. [Black is sort of standard] see https://en.wikipedia.org/wiki/Mandelbrot_set for more info
😉😁😁😁😎🌍☮️