Original code:
In[]:=
(*MikkHeidema'sRecamanSeqfromOEISA005132*)RecamanSeq[i_Integer]:=Fold[With[{lst=Last@#,len=Length@#},Append[#,If[lst>len&&!MemberQ[#,lst-len],lst-len,lst+len]]]&,{0},Range@i];
In[]:=
semiCircularPath[{u_Integer,v_Integer}]:=Withmid=Midpoint[{{u,u},{v,v}}],r=
2
Abs[u-v]2,If[u>v,Circle[mid,r,{-3π/4,π/4}],Circle[mid,r,{π/4,5*π/4}]]In[]:=
paths=semiCircularPath/@Partition[RecamanSeq[800],2,1];
Formula from Math World:
In[]:=
frm=
//ColorNegate;
Header for the video:
In[]:=
ttl=Rasterize[Text[Style[" Recamán Sequence ",20,White,FontFamily->"Copperplate"],Background->Black],RasterSize->720,ImageSize->720]
Out[]=
Sub-header for the video:
In[]:=
sub=Rasterize[Text[Style[ToLowerCase@" Math • Beauty • Music • Reflexivity • History • Memory • Structure • Disorder ",20,White,FontFamily->"Alegreya SC"],Background->Black],RasterSize->720,ImageSize->720]
Out[]=
Check with Manipulate all looks right:
In[]:=
Manipulate[Rasterize[#,RasterSize->720]&@Column[{ttl,#,sub},Spacings->0]&@Graphics[AxisObject[Line[{{0,0},2*{n,n}}],{0,2*n},BaseStyleDirective[White,Opacity[.75]]],{StandardOrange,Opacity[.8],paths[[1;;n]]},Text[Style["Sound ON 🔊",25,Pink,FontFamily->"Didot"],Scaled[{.025,.99}],{Left,Top}],Inset[frm,Scaled[{1,0}],{Right,Bottom},Scaled[.6]],PlotRange->{{-.15n,2n},{-.15n,2*n}},Background->Black,ImagePadding->8,BaseStyle->20,ImageSize->720],{{n,500},1,500,1},SaveDefinitions->True]
Generate video:
In[]:=
v1=Parallelize@AnimationVideo[Rasterize[#,RasterSize->720]&@Column[{ttl,#,sub},Spacings->0]&@Graphics[AxisObject[Line[{{0,0},2*{n,n}}],{0,2*n},BaseStyleDirective[White,Opacity[.75]]],{Orange,paths[[1;;n]]},Text[Style["Sound ON 🔊",25,Pink,FontFamily->"Didot"],Scaled[{.025,.99}],{Left,Top}],Inset[frm,Scaled[{1,0}],{Right,Bottom},Scaled[.6]],PlotRange->{{-.15n,2n},{-.15n,2*n}},Background->Black,ImagePadding->8,BaseStyle->20,ImageSize->720],{n,1,500,1},DefaultDuration->15,RasterSize->720];
Audio from the Wikipedia page:
In[]:=
aud=;
Add audio and format for social media:
Out[]=