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Julia Set Invariant Points
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Hidden Label: "Z" equals "F" left parenthesis, "c" , right parenthesis
Z
=
F
c
Label
equals
=
left parenthesis, 1.6 3 9 , 0.2 1 9 4 , right parenthesis
1
.
6
3
9
,
0
.
2
1
9
4
left parenthesis, negative 0.6 3 9 4 , negative 0.2 1 9 4 , right parenthesis
−
0
.
6
3
9
4
,
−
0
.
2
1
9
4
58
Julia Set:
Julia Set:
59
Expression 60: "z" Subscript, "n" plus 1 , Baseline equals "z" squared plus "c"
z
n
+
1
=
z
2
n
+
c
60
Therefore the invariant points are the solutions of:
Therefore the invariant points are the solutions of:
61
Expression 62: "z" equals "z" squared plus "c"
z
=
z
2
+
c
62
Expression 63: "z" squared minus "z" plus "c" equals 0
z
2
−
z
+
c
=
0
63
Which gives:
Which gives:
64
Expression 65: "z" equals StartFraction, 1 plus-or-minus StartRoot, 1 minus 4 "c" , EndRoot Over 2 , EndFraction
z
=
1
±
1
−
4
c
2
65
Z are our invariant points (there are two for any given c, unless c=1/4).
Z are our invariant points (there are two for any given c, unless c=1/4).
66
67
powered by
powered by
"x"
x
"y"
y
"a" squared
a
2
"a" Superscript, "b" , Baseline
a
b
7
7
8
8
9
9
over
÷
functions
(
(
)
)
less than
<
greater than
>
4
4
5
5
6
6
times
×
| "a" |
|
a
|
,
,
less than or equal to
≤
greater than or equal to
≥
1
1
2
2
3
3
negative
−
A B C
StartRoot, , EndRoot
pi
π
0
0
.
.
equals
=
positive
+
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