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\newcommand{\Sommet}{1.4142135623730951}
\newcommand{\PosFoyer}{2}
\newcommand{\HypAngle}{0}
\setcounter{i}{1}
\newcounter{CoefDiv}\setcounter{CoefDiv}{20}
\newcounter{Inc}\setcounter{Inc}{2}
\newcounter{n}\setcounter{n}{2}
%% , H
%% \Rii=\Ri+2\Sommet ( )
\newcommand{\Ri}{% postscript
\PosFoyer\space\Sommet\space sub \arabic{i}\space\arabic{CoefDiv}\space div add}
\newcommand{\Rii}{\Ri\space\Sommet\space 2 mul add}
\pstGeonode[PosAngle=90]{O}(\PosFoyer,\HypAngle){F}
\pstSymO[PosAngle=180]{O}{F}\pstLineAB{F}{F'}
%%
\pstCircleOA{O}{F}
%% H
\pstGeonode[PosAngle=-135](\Sommet,\HypAngle){S}
\pstGeonode[PosAngle=-45](-\Sommet,\HypAngle){S'}
%% , (FF') S,
%% [FF'] ( H)
\pstRotation[RotAngle=90, PointSymbol=none]{S}{O}[B]
\pstInterLC[PosAngleA=90, PosAngleB=-90]{S}{B}{O}{F}{A_1}{A_2}
\pstLineAB[nodesepA=-3,nodesepB=-5]{A_1}{O}
\pstLineAB[nodesepA=-3,nodesepB=-5]{A_2}{O}
%% cos(\Psi)=OS/OF (c-a-d \Sommet/\PosFoyer)
%% \sqrt(2)/2, \Psi=45 => hyperbole equilatere
\pstMarkAngle[LabelSep=.8, MarkAngleRadius=.7, arrows=->,
LabelSep=1.1]{F}{O}{A_1}{$\Psi$}
\ncline[linecolor=red]{A_1}{A_2}
\pstRightAngle[RightAngleSize=.15]{A_1}{S}{O}
\psset{PointName=none}
\whiledo{\value{n}<8}{%
\psset{RadiusA=\pstDistVal{\Ri},RadiusB=\pstDistVal{\Rii},PointSymbol=none}
\pstInterCC{F}{}{F'}{}{M\arabic{n}}{P\arabic{n}}
\pstInterCC{F'}{}{F}{}{M'\arabic{n}}{P'\arabic{n}}
%% bcp
%% n -> , i ->
%% Inc -> i (2^n)
\stepcounter{n}\addtocounter{i}{\value{Inc}}
\addtocounter{Inc}{\value{Inc}}}%% fin de whiledo
\psset{linecolor=blue}
%%
\pstGenericCurve[GenCurvFirst=S]{M}{2}{7}
\pstGenericCurve[GenCurvFirst=S]{P}{2}{7}
\pstGenericCurve[GenCurvFirst=S']{M'}{2}{7}
\pstGenericCurve[GenCurvFirst=S']{P'}{2}{7}
%%
%\parametricplot[linecolor=black, linewidth=.25\pslinewidth]{-1}{1}
% {t dup tx@EcldDict begin sh exch ch end \Sommet\space mul exch
% \PosFoyer\space dup mul \Sommet\space dup mul sub sqrt mul}
%\parametricplot[linecolor=black, linewidth=.25\pslinewidth]{-1}{1}
% {t dup tx@EcldDict begin sh exch ch end neg \Sommet\space mul exch
% \PosFoyer\space dup mul \Sommet\space dup mul sub sqrt mul}
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