マンデルブロ

f(z)=Az^2+Bz+C
A≠0
Af(z)=A^2z^2+ABz+AC
Af(z)=(Az+B/2)^2-B^2/4+AC
Af(z)+B/2=(Az+B/2)^2-B^2/4+AC+B/2
T(z)=Az+B/2
T(f(z))=T(z)^2-B^2/4+B/2+AC
c=-B^2/4+B/2+AC
T(f(z))=T(z)^2+C
T(z)=Z
g(Z)=Z^2+C
g(Z)=Z
Z=Z^2+C
Zn+1=Zn^2+C
Zn+1-Zn^2=C
Zn+1-Zn^2-C=0
Zn+1=Zn^2+C
Xn+1=Xn^2+C
Xn+1-Xn^2=C
Xn+1-Xn^2-C=0
f(z)=Az^2+Bz+C
A=1
B=0
C=-1
f(z)=z^2-1
Zn+1=Zn^2-(+1)
Z=Z^2-1
0=Z^2-Z-1
Z^2-Z-1=0
Z^2-Z-1=0
x^2-x-1=0
x^2-x=1
(-x)+x^2=1
x-x^2=-1
(1-x)x=-1
t=e^-x=1-x
tx=-1
(-tx)=1
tx=-1
t=e^-x=1-x
(1-x)x=-1
x-x^2=-1
(-x)+x^2=1
x^2-x=1
x^2-x-1=0
Z^2-Z-1=0
Z^2-Z-1=0
t^2-t-1=0
t^2-t=1
(-t)+t^2=1
t-t^2=-1
t(1-t)=-1
x=e^-t=1-t
tx=-1
(-tx)=1
tx=-1
x=e^-t=1-t
t(1-t)=-1
t-t^2=-1
(-t)+t^2=1
t^2-t=1
t^2-t-1=0