Happy "World Tessellation Day"

[BruceH]

June 17th is World Tessellation Day - chosen because it is the birthday of M. C. Escher.

Some light reading: Tessellation Patterns - From Mathematics to Art

If anyone wants to present some calculator generated patterns (50G/Prime/DM42) then please do!

[Gilles]

Is this one for HP50 correct ? The GROB is 500x500 but I forget how to change GROB -> JPG

       
My idea is a kind of "RPL Logo" to get a motif and the to assemble it.

Code:

DIR @ RPL Logo
  ClrScr @ Create a virtuel screen 500x500 pixel, (0,0) in the center
    « #500d DUP BLANK PICT STO PICT SIZE B->R SWAP B->R 
      2. / DUP NEG SWAP XRNG 2. / DUP NEG SWAP YRNG »

  SetAng @ Set Angle 
    « 'AngTrt' STO »
  
  SetPos @ Set turtle pos 
    « 'PosTrt' STO »
  
  RazTrt @ Init Turtle in the center
    « (0 0) SetPos 0 SetAng 99 SF » 

  Raz @ Initialisation  
    « ClrScr DEG ERASE RazTrt  »
      
  Lt @ Tourne gauche : left 
    « 'AngTrt' STO+  »
    
  Rt @ Tourne droite : Right
    « NEG Lt »

  Fw @ Avance : Forward
    « AngTrt DUP2 COS * UNROT SIN * R->C PosTrt + DUP 
      PosTrt IF 99 FS? THEN LINE ELSE DROP2 END 'PosTrt' STO »

  Rpt @ Repeat n time
    « 1 SWAP START DUP EVAL NEXT DROP »
END

And then things like :

Code:

« { 10 Fw  60 Rt } 6 Rpt  » 'Hexa' STO

 Raz  { {  Hexa 60 Rt 20 Fw } 6 Rpt  30 Fw } 6 Rpt

or

Code:

  Raz 
 { { {  Hexa 60 Rt 20 Fw } 6 Rpt  60 Rt 40 Fw } 6 Rpt Hexa 60 Fw } 6 Rpt

etc.

[Allen]

Certainly by now you've seen the "headline" news about the aperiodic "HAT" polykite Einstein? It has some interesting properties. When it was announced, I sat down with pencil and paper to calculate the unit area of each "stone". Somehow that wasn't in any of the papers ( or if it was I missed it? ).

Arxiv: https://arxiv.org/abs/2303.10798

[C.Ret]

Hi,

Sorry, I didn't have time to post this last weekend.

So here is, with a little delay, what to do with the tiling of the infinite plane using your HP-41 provided you know how to aim to print ...

[pier4r]

The patterns on the calculators are pretty neat!