Quote Originally Posted by AntonioLao
The Mandelbrot equation is Zn+1=Zn+C but we can also write it as Zn+1 – C = Zn So, if C=0 then Zn+1=Zn and if Z1=i then Z2 = -1, Z3=1, … This shows the equation visited only three points i,-1, and 1.
If the constant c=0 then as you said we come to Zn+1=Zn^2. But what if instead of i series, we make Zn=n!? In that case, n!+1=Zn^2 that is n!+1=n!^2. The importance of this form o fthe equation is not the possible numbers, but that n!=nx(n-1)x(n-2)x(n-3)...n-n+1 and this relates to the idea of equality whiles getting smaller. A physical version of this would be a tennis ball, if you get the diameter of it and consider it to be n! so every time you add what the 1 is in proportion to it's size, it's circumference will go from diameter times pi then (n!xpy)^2=diameter+1 (1 being a constant ratio proportional to the volume.