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mclarekin committed Nov 23, 2020
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4 changes: 2 additions & 2 deletions handbook.tex
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Mandelbulber End User Manual
% Mandelbulber User Manual
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\newcommand{\mTitle}{Mandelbulber}
\newcommand{\mSubtitle}{End User Manual}
\newcommand{\mSubtitle}{User Manual}
\newcommand{\mVersionDocument}{2.32.0.0}
\newcommand{\mDateDocument}{2020-October}
\newcommand{\mAuthor}{
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6 changes: 3 additions & 3 deletions mandelbulber2/introduction/aboutHandbook.tex
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\section{About this Handbook}
\section{About this Manual}

This handbook has been crafted for both new users and experts to assure confidence and ease of usability for Mandelbulber fractal design. We wish you a Happy Experience!
This user manual covers information for both new and advanced users of the Mandelbulber fractal rendering software.

This handbook is still being written. The most recent version can be downloaded from here: \url{https://github.com/buddhi1980/mandelbulber_doc/releases}
This manual is still being written. The most recent version can be downloaded from here: \url{https://github.com/buddhi1980/mandelbulber_doc/releases}
26 changes: 11 additions & 15 deletions mandelbulber2/manual/chapters/fractals.tex
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\section{What are fractals?}\label{what-are-fractals}

Fractals are objects with self-similarity, where the smaller fragments are
similar to those on a larger scale. A characteristic feature is that the mathematics often produce infinite levels of smaller fractal detail, such that viewing the detail is only limited by the floating point accuracy used in the calculations\index{fractal}
Fractals are mathematical objects where the smaller fragments look
similar to those on a larger scale (called self-similarity). A characteristic feature is that the mathematics often produce infinite levels of smaller fractal detail, such that viewing the detail is only limited by a computer's floating point accuracy used for the calculations\index{fractal}

\subsection{Mandelbrot set}\label{mandelbrot-set}\index{Mandelbrot Set}

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determine if it belongs to the formula specific mathematical fractal set.

The initial value of point \emph{z} is assigned to equal \emph{c}, ($ z_{0} = c
$), this parameter is then used repeatedly in the iteration loop.
$); this parameter is then used repeatedly in the iteration loop.

\begin{center}
\(z_{n + 1} = z_{n}^{2} + c\)
Expand All @@ -52,21 +52,17 @@ \subsection{Mandelbrot set}\label{mandelbrot-set}\index{Mandelbrot Set}
etc.
\end{center}

The program has to determine if these series are convergent. To do this
iterations should be repeated an infinite number of times. But since a computer cannot
infinitely repeat in practice the convergence is determined with a simplification.

Termination conditions are applied to ensure the formula does not iterate to
To do this iterations should be repeated an infinite number of times. But since in practice a computer cannot
infinitely repeat, Termination Conditions are applied to ensure the formula does not iterate to
infinity. The most common conditions used are called \textbf{Bailout} and
\textbf{Maxiter}.

\label{bailout-maxiter}The \textbf{Bailout}\index{termination condition!bailout} condition stops the iteration loop if the formula
transforms (moves) the point further than a set distance away from an
``origin''. This detects if series are convergent (calculated point is outside
the fractal body)
\label{bailout-maxiter}\textbf{Bailout}\index{termination condition!bailout} tests to determine if a point entered into the iteration loop is divergent (trending infinitely outwards), as it will be unlikely to belong to the fractal set. Bailout condition stops the iteration loop if the formula
transforms (moves) the point further than a set distance away from the
origin (typically in 3D, the center xyz coordinates being 0,0,0).

\textbf{Maxiter}\index{termination condition!maxiter} is simply a condition to stop iterating when a maximum numbers
of iterations is reached (just to not do iterations infinite times)
of iterations is reached.

In the Mandelbrot formula, after each iteration, the modulus of a complex number
is calculated; in other words, the length of the vector from the origin
Expand All @@ -90,7 +86,7 @@ \subsection{Mandelbrot set}\label{mandelbrot-set}\index{Mandelbrot Set}

\subsection{3D fractals}\label{d-fractals}

The three dimensional fractal type, the ``Mandelbulb'',\index{Mandelbulb} is calculated from a
The Mandelbulb\index{Mandelbulb} three dimensional fractal is calculated from a
fairly similar pattern to the Mandelbrot set. The difference is that the vector
\emph{z} contains three components (\emph{x}, \emph{y}, \emph{z}) or four
dimensions (\emph{x}, \emph{y}, \emph{z}, \emph{w}). As they are part of the
Expand All @@ -106,7 +102,7 @@ \subsection{3D fractals}\label{d-fractals}
\textbf{then} \emph{z.x} = \emph{something}).

Some other types of 3D fractal objects are based on iterative algorithms (IFS -
Iterated Function Systems\index{IFS}). An example would be the famous Menger Sponge\index{Menger Sponge} (figure \ref{menger_sponge}) or Sierpinski triangle (figure \ref{sierpinski})
Iterated Function Systems\index{IFS}). An example would be the famous Menger Sponge\index{Menger Sponge} (figure \ref{menger_sponge}) or Sierpinski triangle (figure \ref{sierpinski}).
\nopagebreak

\twoImagesWithTwoCaptionsFullWidth{img/manual/media/menger_sponge.png}
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18 changes: 9 additions & 9 deletions mandelbulber2/sound/sound.tex
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\section{Using ``Anim By Sound'' with multiple
tracks}\label{using-anim-by-sound-with-multiple-tracks}
\section{Using ``Animation By Sound'' with multiple
tracks}\label{using-animation-by-sound-with-multiple-tracks}

Note. The following "walk through" tutorial is for using Anim By Sound
Note. The following "walk through" tutorial is for using Animation By Sound
with multiple tracks. This tutorial is based on my initial experiments
with Anim by Sound and may be revised as I gain more experience. The
with Animation by Sound and may be revised as I gain more experience. The
tutorial demonstrates using sound to animate a fractal offset parameter
and the material color. The settings file also includes animation of
some other parameters, and produces an animation just over a minute
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\emph{Note. You can create an audio file for the single purpose of
directing animation, where the audio file is not used at all in the
final song mix. You can use Anim by Sound to create silent videos.}
final song mix. You can use Animation by Sound to create silent videos.}

\emph{Keyframe animation requires changes to be made at keyframes. It is
possible with Sound animation to make changes at any frame, (i.e. a
change at any 1 / 30 of a second time interval, when at 30 fps.)}

\emph{Previously, choreographing parameters with spreadsheets was very
time consuming and I was limited to what I could achieve, so I stopped
and have waited. Anim by Sound has made this process much more simpler,
and have waited. Animation by Sound has made this process much more simpler,
and has infinite possibilities.}

All files used in this example can be downloaded from mandelbulber.org
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field, and select Add to Keyframe Animation.

The parameter will then be listed in the keyframe animation table, with
Anim By Sound in the next column.
Animation By Sound in the next column.

\includegraphics[width=6.69000in,height=2.60000in]{img/sound/media/image3.png}

Expand All @@ -110,7 +110,7 @@ \subsection{Adding a parameter.}\label{adding-a-parameter.}

\subsection{Loading the Audio File}\label{loading-the-audio-file}

Left mouse click on Anim By Sound and the Audio Selector UI will open.
Left mouse click on Animation By Sound and the Audio Selector UI will open.
The name of the parameter will be in the description along the top.

Select an Audio file and three charts will appear.\\
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Add material 1 parameter ``Palette\_offset'' to the Keyframe animation
table.

Open Anim By Sound, load audio file and Enable Animation by sound.
Open Animation By Sound, load audio file and Enable Animation by sound.

Adjust Frequency of interest and bandwidth.

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