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Description:
Equation:
\[ Q_{n} = \frac{1 - Z_{n} + {Z_{0}}^{1024} }{2 + Z_{n}*Z_{0}} \]

\[ \begin{cases}
 & \text{ if } \bigg(Re(Z_{n}) < Im(Z_{n})\bigg) \qquad R_{n}=i*conj(Q_{n}) \\
 & \text{ else }\qquad R_{n} = Q_{n}
\end{cases} \]

\[ Z_{n+1} = R_{n}+C \]

Where:
\[ C=0.5714285714285714-0.5714285714285714*i \]

Escape Occurs When:
The distance between Z_{n} and Z_{0}  is less than 0.5

Iterations:
255

Center of Window:
\[ (-0.44003483333333326, 0.1344042666666669) \]

Window Width:
\[ 4.0*10^{-5} \]
Stats:
Views: 26
Total Favorities: 0 View Who Favorited
Filesize: 1.45MB
Height: 3000 Width: 2400
Discussion Topic: View Topic
Posted by: AlexH September 13, 2018, 02:41:15 AM

Rating: *** by 1 members.
Total Likes: 1

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Comments (3) rss

AlexH
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September 13, 2018, 02:44:03 AM
For some reason I can't edit my gallery posts. I noticed an error. The conditional in the middle of the equations should use an absolute value on the real and imaginary components.
\[ \begin{cases}
 & \text{ if } \bigg(|Re(Z_{n}|) < |Im(Z_{n}|)\bigg) \qquad R_{n}=i*conj(Q_{n}) \\
 & \text{ else }\qquad R_{n} = Q_{n}
\end{cases} \]
AlexH
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September 13, 2018, 02:46:48 AM
Third time's the charm...
The conditional should be on \( Q_{n} \), not \( Z_{n} \).
\[ \begin{cases}
 & \text{ if } \bigg(|Re(Q_{n}|) < |Im(Q_{n}|)\bigg) \qquad R_{n}=i*conj(Q_{n}) \\
 & \text{ else }\qquad R_{n} = Q_{n}
\end{cases} \]
gerson
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September 14, 2018, 08:48:17 PM
Liked it, as usual.

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