Loading ...
Sorry, an error occurred while loading the content.
 

fractal switched Adamson matrix sequence [Fwd: SEQ FROM Roger L. Bagula]

Expand Messages
  • Roger Bagula
    ... Subject: SEQ FROM Roger L. Bagula Date: Tue, 2 Dec 2003 09:30:59 -0500 (EST) From: Reply-To: tftn@earthlink.net To:
    Message 1 of 1 , Dec 2, 2003


      -------- Original Message --------
      Subject:SEQ FROM Roger L. Bagula
      Date:Tue, 2 Dec 2003 09:30:59 -0500 (EST)
      From:<njas@...>
      Reply-To:tftn@...
      To:njas@...
      CC:tftn@...


      The following is a copy of the email message that was sent to njas
      containing the sequence you submitted.
      
      All greater than and less than signs have been replaced by their html
      equivalents.  They will be changed back when the message is processed.
      
      This copy is just for your records.  No reply is expected.
       Subject: NEW SEQUENCE FROM Roger L. Bagula
      
      
      %I A000001
      %S A000001 1,0,1,-1,1,-1,0,-2,-1,-1,-2,0,-2,0,-1,1,0,0,1,-1,1,-1,0,-2,-1,-1,-2,0,-2,0,-1,
      1,0,0,1,-1,1,-1,0,-2,-1,-1,-2,0,-2,0,-1,1,0,0,1,-1,1,-1,0,-2,-1,-1,-2,0,-2,
      0,-1,1,0,0,1,-1,1,-1,0,-2,-1,-1,-2,-1,-2,0,-1,1,0,0,1,0,1,-1,
      0,-2,-1,-1,-2,-1,-2,0,-1,1,0,1,1,1,1,0,1,-1,1,-2,0,-2,-2,-1,-2,0,-2,1,-1,1,0,
      0,1,-1,1,-1,0,-2,-1,-1,-2,0,-2,0,-1,1,0,0,1,-1,1,-1,0,-2,-1,-1,-2,0,-2,0,-1,1,
      0,0,1,-1,1,-1,0,-2,-1,-1,-2,0,-2,0,-1,1,0,0,1,-1,1,-1,0,-2,-1,-1,-2,-1,-2,
      0,-1,1,0,0,1,0,1,-1,0,-2,-1,-1,-2,-1,-2,0,-1,1,0,0,1,0
      %N A000001 A switched recursive matrix method of producing a sequence based on the golden
       mean and the minimal Pisot real roots.
      %C A000001 A switch based on a method using recursive matrices based on a private 
      communication from Gary Adamson. This method of producing sequences is also 
      mentioned in a Curtis McMullen paper dealing with the irrational rotations 
      associated with Siegel disks. The result is a fractal integer sequence of type 
      ABAB....
      %F A000001 m[n_Integer?Positive] :=If[Mod[n,2]==0,m[n-1].m0,m[n-1].m1]
      m[0] = {{1,0},{0,1}}
      a[n]=Floor[m[n][[2,2]]]
      %t A000001 (* Adamson's matrix functions alternating golden mean and minimal Pisot*)
      digits=200
      NSolve[x^3-x-1==0,x]
      k=-1.32471795724474605
      q=k-1/k
      m0={{0,1},{1,q}}
      NSolve[x^2-x-1==0,x]
      k1=1.6180339887498949
      q1=k1-1/k1
      m1={{0,1},{1,q1}}
      m[n_Integer?Positive] :=If[Mod[n,2]==0,m[n-1].m0,m[n-1].m1]
      m[0] = {{1,0},{0,1}}
      a=Table[Floor[m[n][[2,2]]],{n,1,digits}]
      %O A000001 1
      %K A000001 ,nonn,
      %A A000001 Roger L. Bagula (tftn@...), Dec 02 2003
      RH 
      RA 209.178.164.244
      RU 
      RI 
      
      

      -- 
      Respectfully, Roger L. Bagula
      tftn@..., 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :
      URL :  http://home.earthlink.net/~tftn
      URL :  http://victorian.fortunecity.com/carmelita/435/ 
      
      
    Your message has been successfully submitted and would be delivered to recipients shortly.