The scope of tikz picture~~(in an animation)

I've try to modify the animate of Sieve of Eratosthenes from the code (author: Peter Grill): http://www.texample.net/tikz/examples/eratosthenes-sieve/

All I've done is I removed the title and the texts in the right sides.

But there are some problems here:

• The first frame can work properly, the scope of the picture is exactly what I want
• But from the second frame on, the scope of the picture is smaller, you can see a big vertical space between the title and the picture

HOW to maintain the same scope of the picture with the frist frame?

Here is my code:

    \documentclass[t]{beamer}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usetheme{default}

\usepackage{geometry}

\usepackage{microtype}%       Allow comma into margin in list of primes
\usepackage{xstring}%         String comparison
\usepackage{tikz}%            Drawing
\usetikzlibrary{calc}%        Coordinate calculations
\usetikzlibrary{backgrounds}% Apply shading on background layer
\usepackage{animate}

\begin{document}

\def\NumOfColumns{10}% See note above if product of
\def\NumOfRows{10}%    NumOfColumns and NumOfRows > 100.

%% \FramesToHoldAtEnd should be larger than the number of primes
%% so that they can get highlighted at the end of the process
\def\FrameRate{1}%
\def\FramesToHoldAtStart{1}%
\def\FramesToHoldAtEnd{25}% 25 is enough for 10x10

\def\Scale{0.6}% May need tweaking..

\def\PrimeColor{green!80!red}%  Shade for primes found previously
\def\NewPrimeColor{green!80!red}% Shade for prime just found
\def\NewPrimeText{red}%  Color for primes in list

%% List of Primes is typeset into a \node of this width.
\def\TextWidth{2.0cm}%

% Simplifies code below if we just redefine these two from the
% animate package so that they do don't much.
%\renewenvironment{animateinline}[1]{\begingroup}{\endgroup}%
%\renewcommand{\newframe}[1][]{\newpage}%

%%% ---------------------------------------------------------------
%%% Should not need to adjust anything below this line
%%%
\pgfmathtruncatemacro{\MaxNumber}{\NumOfRows*\NumOfColumns}%
\pgfmathtruncatemacro{\MaxValue}{sqrt(\MaxNumber)}%

% Choose opacity so that we can have the max number of shades
%\pgfmathsetmacro{\Opacity}{1.0/min(5,\MaxValue-1)}%
\pgfmathsetmacro{\Opacity}{0.4}%

%% The Sieve algorithm requires that once a number is marked
%% as non-prime (i.e., was a multiple of some other number)
%% we don't need to check multiples of that number as they
%% have already been marked as non-prime.
%%
%% Usually one would use an array and set a flag.  But since
%% variables with numbers are difficult with TeX, we can
%% define a node named with the number that is non-prime.
%% Then just check that the node exists to see if it was
%% marked as non-prime.

\makeatletter
% Mark number as either "Prime" or "NonPrime".
\newcommand*{\MarkNumber}[2][NonPrime]{\node (#1#2) {}}% #1=prefix, #2=num

\pgfutil@ifundefined{pgf@sh@ns@#1#2}{#4}{#3}%
}

% https://tex.stackexchange.com/questions/20655/how-to-undo-a-def-i-e-need-a-undef-capability
\newcommand*\@nameundef[1]{%
\global\expandafter\let\csname #1\endcsname\@undefined%
}

%% Since we repeat the process from the beginning for the animated
%% version, use this to clear the nodes so that the numbers are
%% not marked as multiples of a number from the previous run.
\newcommand{\ClearAllNumberedNodeNames}{%
\foreach \i in {1,...,\MaxValue}{%
\@nameundef{pgf@sh@ns@NonPrime\i}%
\@nameundef{pgf@sh@ns@Prime\i}%
}%
}
\makeatother

%% The Sieve algorithm skips multiples of numbers already marked as
%% non-prime.  So, to number the individual steps, need to use
%% a counter.
%% i.e., Step 4 is processing multiples of 5 (since we skip 4).
\newcounter{StepNumber}%

%%% ---------------------------------------------------------------
%%%
%%%  Titles and Labels
%%%

\newcommand\ListOfPrimes{}
\IfStrEq{\ListOfPrimes}{}{%
\def\Separator{}%   First member of list of primes
}{%
\def\Separator{, }% Subsequent member of list of primes
}%
%
\FillCellForGivenNumber[#1]{#2};%
\global\edef\ListOfPrimes{\ListOfPrimes\Separator#2}%
\MarkNumber[Prime]{#2};%
}

\newcommand*{\ClearListOfPrimes}{%
\ClearAllNumberedNodeNames;%
\renewcommand{\ListOfPrimes}{}%
}

%%% ---------------------------------------------------------------

%%%
%%% Step 1: Create a list of integers 2...n
%%%
\newcommand*{\DrawGridWithNumbers}{%
\begin{scope}% Add numbers to each node
\draw  (0,-1) -- ($(0,-\NumOfRows-1)$);
\foreach \col in {1,...,\NumOfColumns} {%
\draw  (\col,-1) -- ($(\col,-\NumOfRows-1)$);

\draw  (0,-1) -- (\NumOfColumns,-1);
\foreach \row in {1,...,\NumOfRows}{%
\pgfmathtruncatemacro{\value}{\col+\NumOfColumns*(\row-1)}
\IfEq{\value}{1}{
%% Suppress number 1 from being printed since first
%% step of Sieve of Eratosthenes algorithm is to
%% create a list of integers 2...n
}{
\node at ($(\col,-\row)-(0.5,0.5)$) {\value};
}
\draw (0,-\row-1) -- (\NumOfColumns,-\row-1);
}
}
\end{scope}

%% Since we just drew the grid we should ensure that none
%% of the numbered nodes exist (i.e., that no numbers
%% are marked as non-prime.  And reset list of primes.

\ClearListOfPrimes;
\ClearAllNumberedNodeNames;

%\ShowListOfPrimesNode;
}

\newcommand*{\FillCellForGivenNumber}[2][]{%
%% #1 = fill options
%% #2 = number
%%
\pgfmathtruncatemacro{\Column}{mod(#2,\NumOfColumns)}%
\IfEq{\Column}{0}{\pgfmathtruncatemacro{\Column}{\NumOfColumns}}{}%
\pgfmathtruncatemacro{\Row}{(#2-1)/\NumOfColumns+1}%

\begin{scope}[on background layer]
\fill [#1]
(\Column-1,-\Row) --
($(\Column-1,-\Row)+(1,0)$) --
($(\Column-1,-\Row)+(1,-1)$) --
(\Column-1,-\Row-1) --
cycle;
\end{scope}
}

\newcommand*{\ColorMultiplesOf}[2][0]{%
%% If only 1 arg is given (i.e., #1=0), then
%%     #2 = the multiple for which the coloring is applied
%%
%% If two args are given (i.e., #1 != 0) then
%%     #1 = Value of \MaxMultiple (used for animated version)
%%          In the two arg case we run the entire sequence
%%          from the beginning up until the multiple #1*#2
%%          is reached.

\IfEq{#1}{0}{% Run the entire sequence
\pgfmathtruncatemacro{\MaxMultiple}{\MaxNumber/#2}
}{%            Run sequence up until number given for animating
\def\MaxMultiple{#1}
}

\foreach \i in {2,...,\MaxMultiple} {
\FillCellForGivenNumber[
fill=\NonPrimeColor,
fill opacity=\Opacity
]
}
}

\newcommand*{\BuildFrameInternals}[2][0]{%
%% #1 = current multiple to which to build the pattern up to
%%      if #1=0 and #2=\MaxValue, then we are in an end hold frame
%% #2 = number of whose multiples we are eliminating in this step
%%      if #2=1, then only draw grid (provides hold frame at start)

%%\AddTitleNode;% Print Main title if \AnimateSieve is defined

\DrawGridWithNumbers;
\IfEq{#2}{1}{%
%% This is a hold frame at start so only show grid of numbers
}{%
\IfEq{#2}{2}{%
%% No pre-processing steps to be done in this case
}{%
%% Since we are eliminating multiples of a number
%% other than 2, we need to get the table up to
%% the state where all the multiples of 2...(#2-1)
%% are eliminated.

\pgfmathsetmacro{\PreviousMultiple}{#2 - 1}%
\foreach \n in {2,...,\PreviousMultiple} {%
%% Skip. Multiples are already marked as non-prime
%% since this number is a multiple of a smaller
%% prime.
}{%
%% This is a prime. Mark it as prime, and mark
%% its multiples as non-prime.
\ColorMultiplesOf{\n};
}
}
}

%% Already taken care of in a previous run.  This test
%% is needed to cover the case where the value of the
%% sqrt{NumberOfColumns x NumberOfRows) is not prime.
%% For example: 10x10.
}{%
%% Now eliminate the numbers up to the current state
\ColorMultiplesOf[#1]{#2};
}

%% If we are holding the very final result don't print title.
%% This is the case when #2=\MaxValue and #1=0.
%%
%% Need to do this at the end so that we can access
%% which numbers have been marked as non-prime.

\IfEq{#2}{\MaxValue}{%
%\IfEq{#1}{0}{%
%% This is the final hold frame
%%\SubTitleFinal;

}{%
%% In this case, #2 is not a new prime so
%% correct its color. So, don't add it to the
%% list of primes, but correct ensure its
%% color corresponds to an old prime
\FillCellForGivenNumber[fill=\PrimeColor]{#2};
}{%
%% In this case, #2 is a new prime so
%% add it to the list of primes,
}%
}%

%% But since this is the final hold frame, we need
%% to mark all the numbers not already marked as
%% non-prime as prime. Do one at at time, so that
%% this can be seen in the animation.

\pgfmathtruncatemacro{\StartValue}{\MaxValue+1}%
\foreach \p in {\StartValue,...,\MaxNumber}{%
%% This number has been marked as non-prime
}{%
%% This is a prime
%% Already found this prime earlier.
%% So ensure it has appropriate fill.
}{%
%% New prime: Mark it as such, and
%% break out to complete this frame.
\MarkNumber[Prime]{\p};%
\breakforeach;%
}%
}%
}%
%}{%
%% Not final hold frame, so normal title
%}%
}{%
}%
}%
%%\ShowListOfPrimesNode%
}%

\newcommand*{\BuildFrame}[2][0]{%
%% #1 = current multiple to which to build the pattern up to
%% #2 = number of whose multiples we are eliminating in this step
%%      if #2=1, then only draw grid (provides hold frame at start)
\noindent%
\centering%
\begin{tikzpicture}[yscale=\Scale]%
\BuildFrameInternals[#1]{#2};
\end{tikzpicture}%
%
}%

\newcommand*{\BuildFinalFrame}{%
\noindent%
\centering%
\begin{tikzpicture}[yscale=\Scale]%
%%\AddTitleNode;% Print Main title if \AnimateSieve is defined
\DrawGridWithNumbers;
\foreach \p in {2,...,\MaxValue}{%
}{%
\ColorMultiplesOf{\p};
}%
}%
\pgfmathtruncatemacro{\StartValue}{\MaxValue+1}%
\foreach \p in {\StartValue,...,\MaxNumber}{%
%% This number has already been marked as non-prime
}{%
%% This is a prime. Since we are just printing out
%% the final results we don't distinguish between a
%% newly found prime and a prime found previously.
}%
}%

%\ShowListOfPrimesNode;
\end{tikzpicture}%
%
}

\newcounter{CountK}
\newcounter{CountP}
\newcounter{CurrentMaxMultiplePlusOne}
%

\begin{frame}{Sieve of Eratosthenes}
\begin{animateinline}[autopause,controls, buttonsize=1.2em, buttonbg=1:0.78:0,buttonfg=0.2:0.2:0.2]{\FrameRate}%
\stepcounter{StepNumber}%
\setcounter{CountK}{0}%
\whiledo{\arabic{CountK} < \FramesToHoldAtStart}{%
\BuildFrame[0]{1}% initial hold frame
\newframe[\FrameRate]%
\stepcounter{CountK}%
}%
%
\setcounter{CountK}{2}%
\whiledo{\numexpr\arabic{CountK}-1 < \MaxValue}{%
%% \value{CountK} has already been marked as non-prime.
%% Hence, so so are its multiples, and we can skip it.
}{%
%% Question 1: Should be able to replace three lines following with
%%             this. But then animation seems to skip the loop below
% \pgfmathsetcounter{CurrentMaxMultiplePlusOne}{1+(\MaxNumber/\arabic{CountK})}%
\pgfmathtruncatemacro{\MaxMultiple}{\MaxNumber/\arabic{CountK}}%
\setcounter{CurrentMaxMultiplePlusOne}{\MaxMultiple}%
\stepcounter{CurrentMaxMultiplePlusOne}%
%
\setcounter{CountP}{2}%
\stepcounter{StepNumber}%
%% Question 2: Ideally would prefer to use the following syntax
%%             but this does not even compile!!!   But, an indentical
%%             syntax works in the above \whiledo, where the value of
%%             \MaxValue was also defined by \pgfmathtruncatemacro
%               \whiledo{\numexpr\arabic{CountP}-1 < \MaxMultiple}{%
\whiledo{\arabic{CountP} < \arabic{CurrentMaxMultiplePlusOne}}{%
\BuildFrame[\theCountP]{\theCountK}%
\newframe[\FrameRate]%
\stepcounter{CountP}%
}%
}%
\stepcounter{CountK}%
}%
% At end, add hold frames in case we are looping
%
% There needs to be enough of these so that each of the
% primes (those not colored in) get highlighted at each frame.
%
\setcounter{CountK}{2}%
\whiledo{\numexpr\arabic{CountK}-1 < \FramesToHoldAtEnd}{%
\BuildFrame{\MaxValue}%
\newframe[\FrameRate]%
\stepcounter{CountK}%
}
\end{animateinline}%
\end{frame}
\end{document}


To compile the code may require more memory, I just edit the file texmf.cnf under C:\texlive\2018\texmf.cnf, and add the following code at the end of the file:

main_memory=12435455
extra_mem_top=60000000​
extra_mem_bot=5000000
font_mem_size=5000000
pool_size=5000000
buf_size=5000000


and then compile with XeLaTex

• Could you please consider removing all nonstandard characters from your code? Having them in prevents people from just copying and running your code. – user121799 Sep 16 '18 at 14:26
• Hm, looks like accumulated spurious space. Perhaps by uncommented line ends repeated in some loop. – AlexG Sep 16 '18 at 17:17
• OK, I'v removed all nonstandard characters – xaero Sep 17 '18 at 0:44
• @xaero, your code still doesn't compile. If you have made so many modifications to your settings (latex or editor) that you can run it, please use a online service like "sharelatex" or "overleaf" to make sure it compiles for us too. – koleygr Sep 17 '18 at 1:06
• @koleygr, Sorry, I'v edited the texmf.cnf file under C:\texlive\2018\texmf.cnf and added following code:main_memory=12435455 extra_mem_top=60000000​ extra_mem_bot=5000000 font_mem_size=5000000 pool_size=5000000 buf_size=5000000...Could you please compile the code second or third times may works. – xaero Sep 17 '18 at 1:28