Fdtxjr

Recommendation letter by significant other if you worked with them professionally?

How did Alan Turing break the enigma code using the hint given by the lady in the bar?

How can The Temple of Elementary Evil reliably protect itself against kinetic bombardment?

An alternative proof of an application of Hahn-Banach

Doesn't allowing a user mode program to access kernel space memory and execute the IN and OUT instructions defeat the purpose of having CPU modes?

Does this video of collapsing warehouse shelves show a real incident?

PTIJ: wiping amalek’s memory?

Should I take out a loan for a friend to invest on my behalf?

Shifting between bemols (flats) and diesis (sharps)in the key signature

How to detect if C code (which needs 'extern C') is compiled in C++

Do I really need to have a scientific explanation for my premise?

Are babies of evil humanoid species inherently evil?

Why doesn't this Google Translate ad use the word "Translation" instead of "Translate"?

Definition of Statistic

weren't playing vs didn't play

How to write ı (i without dot) character in pgf-pie

Bash script should only kill those instances of another script's that it has launched

What are some noteworthy "mic-drop" moments in math?

Word for a person who has no opinion about whether god exists

Why would one plane in this picture not have gear down yet?

Why was Goose renamed from Chewie for the Captain Marvel film?

In the quantum hamiltonian, why does kinetic energy turn into an operator while potential doesn't?

Why does liquid water form when we exhale on a mirror?

Distinction between apt-cache and dpkg -l

Animate this Moire pattern. What mathematical tools could be used to analyze this moving pattern?

What is the pattern or relation in this table?Mathematical formula for a patternWhy Does This Summation Pattern Occur?Trying to figure out a Mathematical patternWhat is the pattern for this sequence?Is there a pattern for this sequence?What is the next row of this pattern?Pattern Recognition - How to solve this problem?What type of diagram could this be?What is the pattern in this set of numbers?

1

$begingroup$

For a mathematical art project, I want to animate the following pattern I made on desmos. It seems to be a Moire pattern. However I cannot make the pattern move smoothly and continuously because desmos lacks the computing power.

The pattern is a projection of several roating $3D$ structures mapped to $2D.$

Essentially I made the (moving) shadow of these rotating $3$-dimensional structures.

The pattern consists of:

$4$ boxes that differ by rotations.

I've defined the "waves" in the boxes on desmos with these equations:

$$ e^STlog(x)+e^STlog(y)=1. $$

$$ e^STlog(1-x)+e^STlog(y)=1 $$

$$ e^STlog(x)+e^STlog(1-y)=1 $$

$$ e^STlog(1-x)+e^STlog(1-y)=1, $$

Where $T$ is a continuous slider $Tin[0,1]$ representing the flow of mathematical time.

$S$ gauges the spacing of the curves. For pretty evenly spaced curves I used these $49$ values for $S:$

$$S=15.3039,10.3612,7.9153,6.3793,5.3019,4.4955,3.8656,3.3584,2.9405,2.5903,2.2926,2.0367,1.8146,1.6204,1.4496,1.2983,1.1638,1.04377,.93622,.83959,.75256,.67401,.603,.53871,.48045,.42762,.37969,.33619,.29673,.26094,.22852,.19917,.17265,.14874,.12722,.10791,.090664,.075316,.061733,.049793,.039383,.030399,.0227475,.0163414,.0111008,.0069525,.0038286,.0016664,.0004081. $$

So essentially there should be $2N$ fluctuating waves inside each box. $N$ waves are attached to the ends of the box $(0,0)$ and $(1,1)$ and the other $N$ are attached to $(0,1)$ and $(1,0).$ Each half of the waves are spaced evenly apart along the diagonals of the box.

In the images there are $392$ curves.

In the animation each of the waves should move at the same constant velocity as they propagate through the box.

The boxes could also rotate. That would be cool.

Requests:

$1)$ What mathematical tools could I use to analyze this moving pattern?

$2)$ Please animate this pattern.

A picture of the animation frozen at time, $T_1:$

geometry visualization pattern-recognition

share|cite|improve this question

edited 2 days ago

Ultradark

asked 2 days ago

UltradarkUltradark

2881518

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Nice pattern. I have taken the liberty to suppress the tag "harmonic functions" which is related to functions such that their laplacian is $0$ which a priori have not their place here.
  $endgroup$
  – Jean Marie
  2 days ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Okay sounds good
  $endgroup$
  – Ultradark
  2 days ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  There is a "bible" on Moiré patterns "The Theory of the Moiré Phenomenon" in 2 volumes by Isaac Amidror, a researcher in EPFL (Switzerland).
  $endgroup$
  – Jean Marie
  2 days ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you for the reference.
  $endgroup$
  – Ultradark
  2 days ago
  

  
  
  
  

add a comment | 

1

$begingroup$

For a mathematical art project, I want to animate the following pattern I made on desmos. It seems to be a Moire pattern. However I cannot make the pattern move smoothly and continuously because desmos lacks the computing power.

The pattern is a projection of several roating $3D$ structures mapped to $2D.$

Essentially I made the (moving) shadow of these rotating $3$-dimensional structures.

The pattern consists of:

$4$ boxes that differ by rotations.

I've defined the "waves" in the boxes on desmos with these equations:

$$ e^STlog(x)+e^STlog(y)=1. $$

$$ e^STlog(1-x)+e^STlog(y)=1 $$

$$ e^STlog(x)+e^STlog(1-y)=1 $$

$$ e^STlog(1-x)+e^STlog(1-y)=1, $$

Where $T$ is a continuous slider $Tin[0,1]$ representing the flow of mathematical time.

$S$ gauges the spacing of the curves. For pretty evenly spaced curves I used these $49$ values for $S:$

$$S=15.3039,10.3612,7.9153,6.3793,5.3019,4.4955,3.8656,3.3584,2.9405,2.5903,2.2926,2.0367,1.8146,1.6204,1.4496,1.2983,1.1638,1.04377,.93622,.83959,.75256,.67401,.603,.53871,.48045,.42762,.37969,.33619,.29673,.26094,.22852,.19917,.17265,.14874,.12722,.10791,.090664,.075316,.061733,.049793,.039383,.030399,.0227475,.0163414,.0111008,.0069525,.0038286,.0016664,.0004081. $$

So essentially there should be $2N$ fluctuating waves inside each box. $N$ waves are attached to the ends of the box $(0,0)$ and $(1,1)$ and the other $N$ are attached to $(0,1)$ and $(1,0).$ Each half of the waves are spaced evenly apart along the diagonals of the box.

In the images there are $392$ curves.

In the animation each of the waves should move at the same constant velocity as they propagate through the box.

The boxes could also rotate. That would be cool.

Requests:

$1)$ What mathematical tools could I use to analyze this moving pattern?

$2)$ Please animate this pattern.

A picture of the animation frozen at time, $T_1:$

geometry visualization pattern-recognition

share|cite|improve this question

edited 2 days ago

Ultradark

asked 2 days ago

UltradarkUltradark

2881518

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Nice pattern. I have taken the liberty to suppress the tag "harmonic functions" which is related to functions such that their laplacian is $0$ which a priori have not their place here.
  $endgroup$
  – Jean Marie
  2 days ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Okay sounds good
  $endgroup$
  – Ultradark
  2 days ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  There is a "bible" on Moiré patterns "The Theory of the Moiré Phenomenon" in 2 volumes by Isaac Amidror, a researcher in EPFL (Switzerland).
  $endgroup$
  – Jean Marie
  2 days ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you for the reference.
  $endgroup$
  – Ultradark
  2 days ago
  

  
  
  
  

add a comment | 

$begingroup$

For a mathematical art project, I want to animate the following pattern I made on desmos. It seems to be a Moire pattern. However I cannot make the pattern move smoothly and continuously because desmos lacks the computing power.

The pattern is a projection of several roating $3D$ structures mapped to $2D.$

Essentially I made the (moving) shadow of these rotating $3$-dimensional structures.

The pattern consists of:

$4$ boxes that differ by rotations.

I've defined the "waves" in the boxes on desmos with these equations:

$$ e^STlog(x)+e^STlog(y)=1. $$

$$ e^STlog(1-x)+e^STlog(y)=1 $$

$$ e^STlog(x)+e^STlog(1-y)=1 $$

$$ e^STlog(1-x)+e^STlog(1-y)=1, $$

Where $T$ is a continuous slider $Tin[0,1]$ representing the flow of mathematical time.

$S$ gauges the spacing of the curves. For pretty evenly spaced curves I used these $49$ values for $S:$

$$S=15.3039,10.3612,7.9153,6.3793,5.3019,4.4955,3.8656,3.3584,2.9405,2.5903,2.2926,2.0367,1.8146,1.6204,1.4496,1.2983,1.1638,1.04377,.93622,.83959,.75256,.67401,.603,.53871,.48045,.42762,.37969,.33619,.29673,.26094,.22852,.19917,.17265,.14874,.12722,.10791,.090664,.075316,.061733,.049793,.039383,.030399,.0227475,.0163414,.0111008,.0069525,.0038286,.0016664,.0004081. $$

So essentially there should be $2N$ fluctuating waves inside each box. $N$ waves are attached to the ends of the box $(0,0)$ and $(1,1)$ and the other $N$ are attached to $(0,1)$ and $(1,0).$ Each half of the waves are spaced evenly apart along the diagonals of the box.

In the images there are $392$ curves.

In the animation each of the waves should move at the same constant velocity as they propagate through the box.

The boxes could also rotate. That would be cool.

Requests:

$1)$ What mathematical tools could I use to analyze this moving pattern?

$2)$ Please animate this pattern.

A picture of the animation frozen at time, $T_1:$

geometry visualization pattern-recognition

share|cite|improve this question

edited 2 days ago

Ultradark

asked 2 days ago

UltradarkUltradark

2881518

$endgroup$

share|cite|improve this question

edited 2 days ago

Ultradark

asked 2 days ago

UltradarkUltradark

2881518

share|cite|improve this question

edited 2 days ago

Ultradark

asked 2 days ago

UltradarkUltradark

2881518

asked 2 days ago

UltradarkUltradark

2881518

asked 2 days ago

UltradarkUltradark

2881518