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1. manunrd82
   Member
   Posted 1 year ago #
   

   Hi, I'm trying to find all the rules that make a pinwheel tiling in order toget a gc script.
   I'm writing whatever important I find so that maybe you can give me your feedback....
   I think there are several way to get it:
   1_ draw a triangle and subdivided it into 5 similar triangles.
   2_Draw one triangle and starting with rotations, translations and reflections.

   STEP 1: drawing a pinwheel triangle (1,2,?5)
   STEP 2a : rotate it with certain angles that, (I guess are different dipending on the position of the first triangle)
   STEP 2b : divide it into 5 similar smaller triangles
   STEP 3 : scale the resulting triangle composed of 5 other triangle with a scale factor of ?5
   STEP 4 :so on...

   What is not clear yet is the starting point....draw and subdivide a triangle or draw it and rotate with angles as arct (0,5) ???
   Thx
   Manu

2. manunrd82
   Member
   Posted 1 year ago #
   

   
   

3. manunrd82
   Member
   Posted 1 year ago #
   

   
   

4. manunrd82
   Member
   Posted 1 year ago #
   

   Maybe I got it. Keeping what I have written in the previous e-maiI I think that depending on the position of the first triangle we have, the Iterations are similar but different in the angle of rotation:
   The possible angles are really similar to the anglesof a triangle: 30°-60°-90° that correspond about respectively to arctg (1/2)=0,46 Rad= 23,36° ; [pi/2 - arctg (1/2)]=1,57-0,46=1,11 Rad= 63,6° and
   pi/2=1,57 Rad=89,95°

   But these rotations always happens after a horizontal/vertical flip

   If you look at the example that I have attached here you can see that the first triangle has been firstly flip vertically and after rotated of arctg(1/2).....

   What do you think?
   I have tried also with another position of the first triangleand seen that had to be flip horizontally and after rotated of pi/2

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