Cleaning up figure placement in Beamer/minipage

Question

I've placed three figures on the same page through the minipage option. However, it looks quite ugly right now.

My latex (beamer) code for this page looks like:

\frame{
\frametitle{Various initial conditions}
% 
% Nomenclature:
% \begin{align}
%  1-0.05(\cos [2 \pi x/L]+\sin [2 \pi x/L])\underbrace{\cos[2 \pi y/L]}_\text{Trailing term}
% \end{align}

\begin{center}
 \begin{figure}[ht] 

\begin{minipage}[b]{0.35\linewidth}\includegraphics[width=.65\linewidth]{/home/dnaneet/Research/Dissertation/wigner/ic/L=lambda/dftdata/L_lambda_max_1wl_zg_E_0001_Cos_profile_0}
\caption{$1-0.05(\cos [2 \pi x/L]+\sin [2 \pi x/L])\cos[2 \pi y/L]$} 
\end{minipage}
\begin{minipage}[b]{0.35\linewidth}\includegraphics[width=.65\linewidth]{/home/dnaneet/Research/Dissertation/wigner/ic/L=lambda/dftdata/L_lambda_max_1wl_zg_E_0001_Sin_profile_0}
\caption{{\tiny $1 - 0.05(\cos [2 \pi x/L] + \sin [2 \pi x/L]) \sin[2 \pi y/L]$}}  
\end{minipage} \\
\begin{minipage}[b]{0.35\linewidth}\includegraphics[width=.65\linewidth]{/home/dnaneet/Research/Dissertation/wigner/ic/L=lambda/dftdata/L_lambda_max_1wl_zg_E_0001_Cos_rot45_profile_0}
\caption{{\tiny $1 - 0.05(\cos [2 \pi (x+y/\sqrt{2}L)] + \sin [2 \pi (x+y/\sqrt{2}L)]) (\cos[2 \pi (x-y/\sqrt{2}L)])$}}  
\end{minipage}




\end{figure}
\end{center}




} 

And the figures look like:

Any suggestions on how I can clean this up? I also find that the figure caption has too many spaces between the math symbols. Whats up with that?

My preample is:

\documentclass{beamer}

\usepackage{graphicx}
\usepackage{subfigure}
\usepackage{subfig}
\usepackage{epstopdf}
\usepackage{hyperref}
\usepackage{amsmath}
\usepackage[labelformat=empty]{caption}
\usepackage{setspace}
\usepackage[T1]{fontenc}
\usepackage[super,numbers,sort&compress]{natbib}
\usepackage{caption}
% \captionsetup{labelformat=empty,labelsep=none}
% \usepackage{makeidx}
% \usepackage{sidecap}

\setbeamertemplate{footline}[page number]
\setbeamercolor{structure}{bg=yellow, fg=black}

Answer 1

How about this?

\documentclass{beamer}

\usepackage{subcaption}
\usecolortheme{wolverine}

\usepackage{tikz}
%\usepackage{graphicx}

\begin{document}

\begin{frame}
\frametitle{Various initial conditions}
    \centering
    \begin{figure}
        \centering
        \begin{subfigure}[b]{0.45\textwidth}
        \centering
            \begin{tikzpicture}
                \path[draw=red,fill=red!20] (0,0) rectangle (3,3);
            \end{tikzpicture}
            \newline
            \tiny Red-square equation:
            $1-0.05(\cos [2 \pi x/L]+\sin [2 \pi x/L])\cos[2 \pi y/L]$
            \phantomsubcaption \label{subfig:red}
        \end{subfigure}%
        \hspace{0.05\textwidth}
        \begin{subfigure}[b]{0.45\textwidth}
        \centering
            \begin{tikzpicture}
                \path[draw=green,fill=green!20] (0,0) rectangle (3,3);
            \end{tikzpicture}
            \newline
            \tiny Green-square equation:
            $1 - 0.05(\cos [2 \pi x/L] + \sin [2 \pi x/L]) \sin[2 \pi y/L]$
            \phantomsubcaption \label{subfig:green}
        \end{subfigure}%
        \vspace{1em}
        \begin{subfigure}[b]{0.45\textwidth}
        \centering
            \begin{tikzpicture}
                \path[draw=blue,fill=blue!20] (0,0) rectangle (3,3);
            \end{tikzpicture}
            \newline
            \tiny Blue-square equation:
            $1 - 0.05(\cos [2 \pi (x+y/\sqrt{2}L)] +
            \sin [2 \pi (x+y/\sqrt{2}L)]) (\cos[2 \pi (x-y/\sqrt{2}L)])$
            \phantomsubcaption \label{subfig:blue}
        \end{subfigure}%
    \end{figure}

\end{frame}

\end{document}