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1. reversi-fun commented on Feb 15, 2024

   

   reversi-fun

   on Feb 15, 2024

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   Attempted Solution Using Ruby for Algebraic Calculations with Symbolic Coefficients

   I attempted to port the solution for this issue to Ruby language, enabling algebraic calculations with symbolic coefficients.
   By doing so,

   • I was able to separate irregularities caused by the irrational number (\sqrt{3}) from the fractal regularity.
   • This approach helps mitigate the impact of floating-point errors.
   • Additionally, defining a class for algebraic calculations made it easier to add verification code based on mathematical properties.

   Feel free to explore this Ruby-based solution and provide feedback!

   https://github.com/reversi-fun/symbolic-spectre-tiles

   coef A = 7.320508075688773		Ratio(0.366)
   coef B = 12.679491924311227		Ratio(0.634)
   
   Mystic_SPECTRE_POINTS = [
   	0+0i, 		(0.0 + 0.0*i),
   	((1.0)*B)+0i, 		(12.6795 + 0.0*i),
   	((1.5)*B)-((0.5)*B*√3)*i, 		(19.0192 + -10.9808*i),
   	((1.5)*B + (0.5)*A*√3)-((-0.5)*A + (0.5)*B*√3)*i, 		(25.359 + -7.3205*i),
   	((1.5)*B + (0.5)*A*√3)+((1.5)*A + (-0.5)*B*√3)*i, 		(25.359 +  **0.0*i**),
   	((2.5)*B + (0.5)*A*√3)+((1.5)*A + (-0.5)*B*√3)*i, 		(38.0385 + **0.0*i**),
   	((3.0)*B + (0.5)*A*√3)+((1.5)*A)*i, 		(44.3782 + 10.9808*i),
   	((3.0)*B)+((2.0)*A)*i, 		(38.0385 + 14.641*i),
   	((3.0)*B + (-0.5)*A*√3)+((1.5)*A)*i, 		(31.6987 + 10.9808*i),
   	((2.5)*B + (-0.5)*A*√3)+((1.5)*A + (0.5)*B*√3)*i, 		(25.359 + 21.9615*i),
   	((1.5)*B + (-0.5)*A*√3)+((1.5)*A + (0.5)*B*√3)*i, 		(12.6795 + 21.9615*i),
   	((0.5)*B + (-0.5)*A*√3)+((1.5)*A + (0.5)*B*√3)*i, 		(0.0 + 21.9615*i),
   	((-0.5)*A*√3)+((1.5)*A)*i, 		(-6.3397 + 10.9808*i),
   	0+((1.0)*A)*i, 		(0.0 + 7.3205*i),
   ]
   
2. chengchu88 commented on Feb 26, 2024

   

   chengchu88

   on Feb 26, 2024

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   thank you both for sharing the code. I gave it a try and still sees the mystic clusters, and so far it seems only works for edge_a=edge_b? wonder how to fix it? thank you!
3. reversi-fun commented on Feb 27, 2024

   

   reversi-fun

   on Feb 27, 2024

   Last edited by reversi-fun

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   @chengchu88
   This issue should have been posted in my repository(symbolic-spectre-tiles).

   it seems only works for edge_a=edge_b?

   There may be a mis-understanding due to the confusion surrounding the following terms:

   • “The Hat”: Refers to the 13-sided polygon that requires its own mirror reflections.
     It family includes { hats or turtles}.
   • “Weakly Chiral Aperiodic Monotile”: Describes the 14-sided polygon where Tile(1,1)
     == Tile(Edge_a,Edge_b) {Edge_a == Edge_b} is a monotile.
   • “Spectres”: Refers to the edges of Tile(Edge_a,Edge_b) that produce a “family of shapes” we call “Spectres.”
     The set includes { (Edge_a ==Edge_b) => “Spectre” , (Edge_a != Edge_b) => {“Chevron,” and “Comet”}}.
     Perhaps what you refer to as “mystic clusters” falls into the category of {“Chevron” or “Comet”}.
     These are all part of the family of “Spectres.”

   wonder how to fix it?

   If it's a bug that can be fixed, I'd like to know how to fix it.
   
   but may be NONE!
   

   I am in the process of confirming that the self-verification function built into (symbolic-spectre-tiles) implements the algorithm shown in the original paper and related articles.
   
   
   If exist Tile(Edge_a,Edge_b) {Edge_a NOT equal to Edge_b} is a monotile,
   I couldn't find a way to fix it from the original paper or its companion article.

   In the tile pattern quoted in the original article, observe the pattern when the Edge_a and Edge_b change continuously.

   • If Edge_a != Edge_b then {{"Chevron" and "Comet"} or {14-sided Hat and Turtle}} are drawn ( NOT monotile,).
   • If Edge_a ==Edge_b only at the moment {"Spectre"} is depicted (monotile) .

   https://cs.uwaterloo.ca/~csk/spectre/examples/anim.gif
   https://www.youtube.com/watch?v=vtpswcAfWiI&t=28s
   https://www.youtube.com/watch?v=3CxF-GkkjiU

   
4. chengchu88 commented on Feb 28, 2024

   

   chengchu88

   on Feb 28, 2024 via email

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   Thank you sir, appreciate your explanation. I did confuse the different implementations as the same matter!

   …

   On Tue, Feb 27, 2024 at 6:44 AM reversi.fun ***@***.***> wrote: @chengchu88 <https://github.com/chengchu88> This issue should have been posted in my repository(symbolic-spectre-tiles <https://github.com/reversi-fun/symbolic-spectre-tiles>). it seems only works for edge_a=edge_b? There may be a misunderstanding due to the confusion surrounding the following terms: - “The Hat”: Refers to the 13-sided polygon that requires its own mirror reflections. It family includes { hats or turtles}. - “Weakly Chiral Aperiodic Monotile”: Describes the 14-sided polygon where Tile(1,1) == Edge_a == Edge_b is a monotile. - “Spectres”: Refers to the edges of Tile(1,1) that produce a “family of shapes” we call “Spectres.” The set includes {“Spectre,” “Chevron,” and “Comet”}. Perhaps what you refer to as “mystic clusters” falls into the category of {“Chevron” or “Comet”}. These are all part of the family of “Spectres.” wonder how to fix it? NONE! The Fix you want doesn't exist in the original paper or in the article of its associates. In the tile pattern quoted in the original article, observe the pattern when the Edge_a and Edge_b change continuously. - If Edge_a != Edge_b then {"Chevron" and "Comet"} are drawn. - If Edge_a ==Edge_b only at the moment {"Spectre"} is depicted . https://cs.uwaterloo.ca/~csk/spectre/examples/anim.gif https://www.youtube.com/watch?v=vtpswcAfWiI&t=28s — Reply to this email directly, view it on GitHub <#3 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AJKLC6H4GFRLMPWCOO4IABLYVXWMTAVCNFSM6AAAAABC7WFHMKVHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMYTSNRWG4YDSNBTHA> . You are receiving this because you were mentioned.Message ID: ***@***.***>