Microscopic Structure of Spherical Elastic Membrane

I would like to draw a 2D network on the surface of a light-grey non-transparent sphere. In the actual fact, the network represents a 2D square lattice composed of many balls and springs as proposed below in TikZ code (by courtesy of @marmot). The idea is to have a spherical elastic membrane capturing an ideal gas inside. The lattice essentially symbolizes the microscopic structure of the membrane.

This question has its roots in the original one:

Drawing a 2D square lattice (springs + balls) on a convex surface

Thank you greatly for the help in advance.

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{decorations.pathmorphing}
\begin{document}
\begin{tikzpicture}
\clip (-1,-1) rectangle (11,11);
\foreach \X in {-2,0,...,10}
{\foreach \Y in {-2,0,...,10}
{\draw[decorate,decoration={coil,aspect=0.5,amplitude=1.5mm, segment
length=1.5mm}] (\X,\Y) -- ++(0,2) -- ++(2,0);
\node[circle,text=white,font=\sffamily\bfseries\large,inner
color=blue,outer color=black] at (\X,\Y) {+};}}
\end{tikzpicture}
\end{document}

• Can you please add a sketch of what you want to achieve? – marmot Dec 18 '18 at 11:52
• The same as the picture from @marmot code (i.stack.imgur.com/Kz0Im.png), but spanned across the entire sphere which is coloured in non-transparent light-grey. – Savchenko Dec 18 '18 at 13:26

Here is a first attempt: solid sphere plus different plot marks. Everything else is as in the last code of this answer.

\documentclass[border=3.14mm,tikz]{standalone}
\usepackage{pgfplots}
\usepackage{xxcolor}
\pgfplotsset{compat=1.16}
\usetikzlibrary{decorations.pathmorphing,decorations.markings}
% Declare nice sphere shading: http://tex.stackexchange.com/a/54239/12440
color(0bp)=(tikz@ball!0!white);
color(7bp)=(tikz@ball!0!white);
color(15bp)=(tikz@ball!70!black);
color(20bp)=(black!70);
color(30bp)=(black!70)}
\makeatother

% Style to set TikZ camera angle, like PGFPlots view
\tikzset{viewport/.style 2 args={
x={({cos(-#1)*1cm},{sin(-#1)*sin(#2)*1cm})},
y={({-sin(-#1)*1cm},{cos(-#1)*sin(#2)*1cm})},
z={(0,{cos(#2)*1cm})}
}}

% Styles to plot only points that are before or behind the sphere.
\pgfplotsset{only foreground/.style={
restrict expr to domain={rawx*\CameraX + rawy*\CameraY + rawz*\CameraZ}{-0.05:100},
}}
\pgfplotsset{only background/.style={
restrict expr to domain={rawx*\CameraX + rawy*\CameraY + rawz*\CameraZ}{-100:0.05}
}}

% Automatically plot transparent lines in background and solid lines in foreground
\addplot3[#1,only background, opacity=0.25] #2;
}

% attempt to do similar things for discrete plots
}

\newcommand{\ViewAzimuth}{-30}
\newcommand{\ViewElevation}{30}

\tikzset{spring/.style={decorate,decoration={coil,aspect=0.5,amplitude=1.5mm, segment
length=1.5mm}}}
% pgfmanual p. 1087
{color(0bp)=(blue!100!black); color(9bp)=(blue!90!black);
color(18bp)=(blue!70!black); color(25bp)=(blue!50!black); color(50bp)=(black)}

\pgfdeclareplotmark{interesting}{\pgfpathcircle{\pgfpoint{0ex}{0ex}}{2ex}
\pgfusepath{}
\pgfpathmoveto{\pgfpoint{0pt}{-5pt}}
\pgfpathlineto{\pgfpoint{0pt}{5pt}}
\pgfpathmoveto{\pgfpoint{-5pt}{0pt}}
\pgfpathlineto{\pgfpoint{5pt}{0pt}}
\pgfsetstrokecolor{white}
\pgfsetlinewidth{0.8pt}
\pgfusepath{stroke}
}
\begin{document}
\begin{tikzpicture}
% Compute camera unit vector for calculating depth
\pgfmathsetmacro{\CameraX}{sin(\ViewAzimuth)*cos(\ViewElevation)}
\pgfmathsetmacro{\CameraY}{-cos(\ViewAzimuth)*cos(\ViewElevation)}
\pgfmathsetmacro{\CameraZ}{sin(\ViewElevation)}
\pgfmathsetmacro{\R}{12}
\path[use as bounding box] (-\R,-\R) rectangle (\R,\R); % Avoid jittering animation
% Draw a nice looking sphere
\begin{scope}
\clip (0,0) circle (\R);
\begin{scope}[transform canvas={rotate=-20}]
\shade [ball color=white] (0,0.5) ellipse (\R*1.8 and \R*1.5);
\end{scope}
\end{scope}
\begin{axis}[
hide axis,
view={\ViewAzimuth}{\ViewElevation},     % Set view angle
every axis plot/.style={very thin},
disabledatascaling,                      % Align PGFPlots coordinates with TikZ
anchor=origin,                           % Align PGFPlots coordinates with TikZ
viewport={\ViewAzimuth}{\ViewElevation}, % Align PGFPlots coordinates with TikZ
]
% plot latitude circles
\pgfplotsinvokeforeach{-75,-45,...,75}
{\addFGBGSampleplot[spring,domain=0:2*pi, samples=51, samples y=1]
({\R*cos(#1)*cos(deg(x))}, {\R*cos(#1)*sin(deg(x))}, {\R*sin(#1)});}
% plot longitude circles
\pgfplotsinvokeforeach{0,30,...,150}
{\addFGBGSampleplot[spring,domain=0:2*pi, samples=51, samples y=1]
({\R*cos(#1)*cos(deg(x))}, {\R*sin(#1)*cos(deg(x))}, {\R*sin(deg(x))});
}
% plot longitude circles
\pgfplotsinvokeforeach{0,30,...,330}