Mixing
What is the function for a 'fractal sine wave'?
$begingroup$
Maybe I abused the word fractal here. I was wondering what's the function ( if not functions ) for this wave:
My attempt was this function, It looks the same, but It's not.
The second sine wave is following the envelope of the first, somewhat following the 90-degree angle of the first sine wave.
$y=frac{sin(200*x)}{10}+sin(x)$
functions approximation
edited Oct 23 '15 at 20:42
Zach466920
6,23111142
asked Oct 17 '15 at 13:25
Muhamed KrlićMuhamed Krlić
14817
$endgroup$
add a comment |
$begingroup$
Maybe I abused the word fractal here. I was wondering what's the function ( if not functions ) for this wave:
My attempt was this function, It looks the same, but It's not.
The second sine wave is following the envelope of the first, somewhat following the 90-degree angle of the first sine wave.
$y=frac{sin(200*x)}{10}+sin(x)$
functions approximation
edited Oct 23 '15 at 20:42
Zach466920
6,23111142
asked Oct 17 '15 at 13:25
Muhamed KrlićMuhamed Krlić
14817
$endgroup$
$begingroup$
PS: Sorry the axis weren't proportional.
$endgroup$
– Muhamed Krlić
Oct 17 '15 at 13:28
2
$begingroup$
That doesn't even look like a function -- it goes backwards near the middle of your plot.
$endgroup$
– Henning Makholm
Oct 17 '15 at 13:29
add a comment |
$begingroup$
Maybe I abused the word fractal here. I was wondering what's the function ( if not functions ) for this wave:
My attempt was this function, It looks the same, but It's not.
The second sine wave is following the envelope of the first, somewhat following the 90-degree angle of the first sine wave.
$y=frac{sin(200*x)}{10}+sin(x)$
functions approximation
edited Oct 23 '15 at 20:42
Zach466920
6,23111142
asked Oct 17 '15 at 13:25
Muhamed KrlićMuhamed Krlić
14817
$endgroup$
Maybe I abused the word fractal here. I was wondering what's the function ( if not functions ) for this wave:
My attempt was this function, It looks the same, but It's not.
The second sine wave is following the envelope of the first, somewhat following the 90-degree angle of the first sine wave.
$y=frac{sin(200*x)}{10}+sin(x)$
functions approximation
functions approximation
edited Oct 23 '15 at 20:42
Zach466920
6,23111142
asked Oct 17 '15 at 13:25
Muhamed KrlićMuhamed Krlić
14817
edited Oct 23 '15 at 20:42
Zach466920
6,23111142
asked Oct 17 '15 at 13:25
Muhamed KrlićMuhamed Krlić
14817
edited Oct 23 '15 at 20:42
Zach466920
6,23111142
edited Oct 23 '15 at 20:42
Zach466920
6,23111142
edited Oct 23 '15 at 20:42
Zach466920
6,23111142
6,23111142
asked Oct 17 '15 at 13:25
Muhamed KrlićMuhamed Krlić
14817
asked Oct 17 '15 at 13:25
Muhamed KrlićMuhamed Krlić
14817
asked Oct 17 '15 at 13:25
Muhamed KrlićMuhamed Krlić
14817
14817
$begingroup$
PS: Sorry the axis weren't proportional.
$endgroup$
– Muhamed Krlić
Oct 17 '15 at 13:28
2
$begingroup$
That doesn't even look like a function -- it goes backwards near the middle of your plot.
$endgroup$
– Henning Makholm
Oct 17 '15 at 13:29
add a comment |
$begingroup$
PS: Sorry the axis weren't proportional.
$endgroup$
– Muhamed Krlić
Oct 17 '15 at 13:28
2
$begingroup$
That doesn't even look like a function -- it goes backwards near the middle of your plot.
$endgroup$
– Henning Makholm
Oct 17 '15 at 13:29
$begingroup$
PS: Sorry the axis weren't proportional.
$endgroup$
– Muhamed Krlić
Oct 17 '15 at 13:28
$begingroup$
PS: Sorry the axis weren't proportional.
$endgroup$
– Muhamed Krlić
Oct 17 '15 at 13:28
2
2
$begingroup$
That doesn't even look like a function -- it goes backwards near the middle of your plot.
$endgroup$
– Henning Makholm
Oct 17 '15 at 13:29
$begingroup$
That doesn't even look like a function -- it goes backwards near the middle of your plot.
$endgroup$
– Henning Makholm
Oct 17 '15 at 13:29
add a comment |
3 Answers
3
active
oldest
votes
$begingroup$
Probably not what you had in mind, but this is what you get with the parametric equation below:
$$x=t-frac{cos(t)}{sqrt{1+cos^2(t)}}0.15sin(12t)\
y=sin(t)+frac1{sqrt{1+cos^2(t)}}0.15sin(12t)$$
answered Oct 17 '15 at 13:42
Yves DaoustYves Daoust
129k675227
$endgroup$
$begingroup$
I think this is what I was looking for.
$endgroup$
– Muhamed Krlić
Oct 17 '15 at 13:46
$begingroup$
Which was gotten by computing the upwards unit normal vector, scaling by $0.15sin(12t)$ (because the small waves go through 12 periods while the main sine wave goes through 1 in the original graphic, and eyeballing the figure $0.15$), then adding it to the original parametrization.
$endgroup$
– whacka
Oct 17 '15 at 13:48
1
$begingroup$
@whacka: obviously :) If you feel in a good shape, you can derive the equation with an added third generation wave :)
$endgroup$
– Yves Daoust
Oct 17 '15 at 13:49
add a comment |
$begingroup$
If you are actually looking for a fractal sine wave, you probably mean this function from Weierstrauss:
$$f(x)=sum_{n=0}^{infty}left(frac 23right)^ncos(9^npi x)$$
The main fame of this function is that it is continuous everywhere but differentiable nowhere.
Here are the first four partial sums of that series, for $n=0,1,2,3$. The graph you show is similar to the second one, which has the equation
$$f1(x)=cos(pi x)+frac 23cos(9pi x)$$
answered Oct 17 '15 at 13:42
Rory DaultonRory Daulton
29.5k63355
$endgroup$
add a comment |
$begingroup$
Perhaps you are looking for functions of the form
$y=asin(bx)+csin(dx)$
with $a,b,c,d$ positive constants.
For example: Try $a=1,b=1,c=.3,d=12$ to start with -- and play around with it till it matches your purpose.
answered Oct 17 '15 at 13:34
OnceUponACrinoidOnceUponACrinoid
73136
$endgroup$
$begingroup$
Sorry, I mistyped my formula. This is what I already tried.
$endgroup$
– Muhamed Krlić
Oct 17 '15 at 13:42
add a comment |
Your Answer
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Probably not what you had in mind, but this is what you get with the parametric equation below:
$$x=t-frac{cos(t)}{sqrt{1+cos^2(t)}}0.15sin(12t)\
y=sin(t)+frac1{sqrt{1+cos^2(t)}}0.15sin(12t)$$
answered Oct 17 '15 at 13:42
Yves DaoustYves Daoust
129k675227
$endgroup$
$begingroup$
I think this is what I was looking for.
$endgroup$
– Muhamed Krlić
Oct 17 '15 at 13:46
$begingroup$
Which was gotten by computing the upwards unit normal vector, scaling by $0.15sin(12t)$ (because the small waves go through 12 periods while the main sine wave goes through 1 in the original graphic, and eyeballing the figure $0.15$), then adding it to the original parametrization.
$endgroup$
– whacka
Oct 17 '15 at 13:48
1
$begingroup$
@whacka: obviously :) If you feel in a good shape, you can derive the equation with an added third generation wave :)
$endgroup$
– Yves Daoust
Oct 17 '15 at 13:49
add a comment |
$begingroup$
Probably not what you had in mind, but this is what you get with the parametric equation below:
$$x=t-frac{cos(t)}{sqrt{1+cos^2(t)}}0.15sin(12t)\
y=sin(t)+frac1{sqrt{1+cos^2(t)}}0.15sin(12t)$$
answered Oct 17 '15 at 13:42
Yves DaoustYves Daoust
129k675227
$endgroup$
$begingroup$
I think this is what I was looking for.
$endgroup$
– Muhamed Krlić
Oct 17 '15 at 13:46
$begingroup$
Which was gotten by computing the upwards unit normal vector, scaling by $0.15sin(12t)$ (because the small waves go through 12 periods while the main sine wave goes through 1 in the original graphic, and eyeballing the figure $0.15$), then adding it to the original parametrization.
$endgroup$
– whacka
Oct 17 '15 at 13:48
1
$begingroup$
@whacka: obviously :) If you feel in a good shape, you can derive the equation with an added third generation wave :)
$endgroup$
– Yves Daoust
Oct 17 '15 at 13:49
add a comment |
$begingroup$
Probably not what you had in mind, but this is what you get with the parametric equation below:
$$x=t-frac{cos(t)}{sqrt{1+cos^2(t)}}0.15sin(12t)\
y=sin(t)+frac1{sqrt{1+cos^2(t)}}0.15sin(12t)$$
answered Oct 17 '15 at 13:42
Yves DaoustYves Daoust
129k675227
$endgroup$
Probably not what you had in mind, but this is what you get with the parametric equation below:
$$x=t-frac{cos(t)}{sqrt{1+cos^2(t)}}0.15sin(12t)\
y=sin(t)+frac1{sqrt{1+cos^2(t)}}0.15sin(12t)$$
answered Oct 17 '15 at 13:42
Yves DaoustYves Daoust
129k675227
answered Oct 17 '15 at 13:42
Yves DaoustYves Daoust
129k675227
answered Oct 17 '15 at 13:42
Yves DaoustYves Daoust
129k675227
answered Oct 17 '15 at 13:42
Yves DaoustYves Daoust
129k675227
129k675227
$begingroup$
I think this is what I was looking for.
$endgroup$
– Muhamed Krlić
Oct 17 '15 at 13:46
$begingroup$
Which was gotten by computing the upwards unit normal vector, scaling by $0.15sin(12t)$ (because the small waves go through 12 periods while the main sine wave goes through 1 in the original graphic, and eyeballing the figure $0.15$), then adding it to the original parametrization.
$endgroup$
– whacka
Oct 17 '15 at 13:48
1
$begingroup$
@whacka: obviously :) If you feel in a good shape, you can derive the equation with an added third generation wave :)
$endgroup$
– Yves Daoust
Oct 17 '15 at 13:49
add a comment |
$begingroup$
I think this is what I was looking for.
$endgroup$
– Muhamed Krlić
Oct 17 '15 at 13:46
$begingroup$
Which was gotten by computing the upwards unit normal vector, scaling by $0.15sin(12t)$ (because the small waves go through 12 periods while the main sine wave goes through 1 in the original graphic, and eyeballing the figure $0.15$), then adding it to the original parametrization.
$endgroup$
– whacka
Oct 17 '15 at 13:48
1
$begingroup$
@whacka: obviously :) If you feel in a good shape, you can derive the equation with an added third generation wave :)
$endgroup$
– Yves Daoust
Oct 17 '15 at 13:49
$begingroup$
I think this is what I was looking for.
$endgroup$
– Muhamed Krlić
Oct 17 '15 at 13:46
$begingroup$
I think this is what I was looking for.
$endgroup$
– Muhamed Krlić
Oct 17 '15 at 13:46
$begingroup$
Which was gotten by computing the upwards unit normal vector, scaling by $0.15sin(12t)$ (because the small waves go through 12 periods while the main sine wave goes through 1 in the original graphic, and eyeballing the figure $0.15$), then adding it to the original parametrization.
$endgroup$
– whacka
Oct 17 '15 at 13:48
$begingroup$
Which was gotten by computing the upwards unit normal vector, scaling by $0.15sin(12t)$ (because the small waves go through 12 periods while the main sine wave goes through 1 in the original graphic, and eyeballing the figure $0.15$), then adding it to the original parametrization.
$endgroup$
– whacka
Oct 17 '15 at 13:48
1
1
$begingroup$
@whacka: obviously :) If you feel in a good shape, you can derive the equation with an added third generation wave :)
$endgroup$
– Yves Daoust
Oct 17 '15 at 13:49
$begingroup$
@whacka: obviously :) If you feel in a good shape, you can derive the equation with an added third generation wave :)
$endgroup$
– Yves Daoust
Oct 17 '15 at 13:49
add a comment |
$begingroup$
If you are actually looking for a fractal sine wave, you probably mean this function from Weierstrauss:
$$f(x)=sum_{n=0}^{infty}left(frac 23right)^ncos(9^npi x)$$
The main fame of this function is that it is continuous everywhere but differentiable nowhere.
Here are the first four partial sums of that series, for $n=0,1,2,3$. The graph you show is similar to the second one, which has the equation
$$f1(x)=cos(pi x)+frac 23cos(9pi x)$$
answered Oct 17 '15 at 13:42
Rory DaultonRory Daulton
29.5k63355
$endgroup$
add a comment |
$begingroup$
If you are actually looking for a fractal sine wave, you probably mean this function from Weierstrauss:
$$f(x)=sum_{n=0}^{infty}left(frac 23right)^ncos(9^npi x)$$
The main fame of this function is that it is continuous everywhere but differentiable nowhere.
Here are the first four partial sums of that series, for $n=0,1,2,3$. The graph you show is similar to the second one, which has the equation
$$f1(x)=cos(pi x)+frac 23cos(9pi x)$$
answered Oct 17 '15 at 13:42
Rory DaultonRory Daulton
29.5k63355
$endgroup$
add a comment |
$begingroup$
If you are actually looking for a fractal sine wave, you probably mean this function from Weierstrauss:
$$f(x)=sum_{n=0}^{infty}left(frac 23right)^ncos(9^npi x)$$
The main fame of this function is that it is continuous everywhere but differentiable nowhere.
Here are the first four partial sums of that series, for $n=0,1,2,3$. The graph you show is similar to the second one, which has the equation
$$f1(x)=cos(pi x)+frac 23cos(9pi x)$$
answered Oct 17 '15 at 13:42
Rory DaultonRory Daulton
29.5k63355
$endgroup$
If you are actually looking for a fractal sine wave, you probably mean this function from Weierstrauss:
$$f(x)=sum_{n=0}^{infty}left(frac 23right)^ncos(9^npi x)$$
The main fame of this function is that it is continuous everywhere but differentiable nowhere.
Here are the first four partial sums of that series, for $n=0,1,2,3$. The graph you show is similar to the second one, which has the equation
$$f1(x)=cos(pi x)+frac 23cos(9pi x)$$
answered Oct 17 '15 at 13:42
Rory DaultonRory Daulton
29.5k63355
answered Oct 17 '15 at 13:42
Rory DaultonRory Daulton
29.5k63355
answered Oct 17 '15 at 13:42
Rory DaultonRory Daulton
29.5k63355
answered Oct 17 '15 at 13:42
Rory DaultonRory Daulton
29.5k63355
29.5k63355
add a comment |
add a comment |
$begingroup$
Perhaps you are looking for functions of the form
$y=asin(bx)+csin(dx)$
with $a,b,c,d$ positive constants.
For example: Try $a=1,b=1,c=.3,d=12$ to start with -- and play around with it till it matches your purpose.
answered Oct 17 '15 at 13:34
OnceUponACrinoidOnceUponACrinoid
73136
$endgroup$
$begingroup$
Sorry, I mistyped my formula. This is what I already tried.
$endgroup$
– Muhamed Krlić
Oct 17 '15 at 13:42
add a comment |
$begingroup$
Perhaps you are looking for functions of the form
$y=asin(bx)+csin(dx)$
with $a,b,c,d$ positive constants.
For example: Try $a=1,b=1,c=.3,d=12$ to start with -- and play around with it till it matches your purpose.
answered Oct 17 '15 at 13:34
OnceUponACrinoidOnceUponACrinoid
73136
$endgroup$
$begingroup$
Sorry, I mistyped my formula. This is what I already tried.
$endgroup$
– Muhamed Krlić
Oct 17 '15 at 13:42
add a comment |
$begingroup$
Perhaps you are looking for functions of the form
$y=asin(bx)+csin(dx)$
with $a,b,c,d$ positive constants.
For example: Try $a=1,b=1,c=.3,d=12$ to start with -- and play around with it till it matches your purpose.
answered Oct 17 '15 at 13:34
OnceUponACrinoidOnceUponACrinoid
73136
$endgroup$
Perhaps you are looking for functions of the form
$y=asin(bx)+csin(dx)$
with $a,b,c,d$ positive constants.
For example: Try $a=1,b=1,c=.3,d=12$ to start with -- and play around with it till it matches your purpose.
answered Oct 17 '15 at 13:34
OnceUponACrinoidOnceUponACrinoid
73136
answered Oct 17 '15 at 13:34
OnceUponACrinoidOnceUponACrinoid
73136
answered Oct 17 '15 at 13:34
OnceUponACrinoidOnceUponACrinoid
73136
answered Oct 17 '15 at 13:34
OnceUponACrinoidOnceUponACrinoid
73136
73136
$begingroup$
Sorry, I mistyped my formula. This is what I already tried.
$endgroup$
– Muhamed Krlić
Oct 17 '15 at 13:42
add a comment |
$begingroup$
Sorry, I mistyped my formula. This is what I already tried.
$endgroup$
– Muhamed Krlić
Oct 17 '15 at 13:42
$begingroup$
Sorry, I mistyped my formula. This is what I already tried.
$endgroup$
– Muhamed Krlić
Oct 17 '15 at 13:42
$begingroup$
Sorry, I mistyped my formula. This is what I already tried.
$endgroup$
– Muhamed Krlić
Oct 17 '15 at 13:42
add a comment |
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$begingroup$
PS: Sorry the axis weren't proportional.
$endgroup$
– Muhamed Krlić
Oct 17 '15 at 13:28
2
$begingroup$
That doesn't even look like a function -- it goes backwards near the middle of your plot.
$endgroup$
– Henning Makholm
Oct 17 '15 at 13:29