Why's the Graph of $y = sin (cos (e^x))$ so Wonky? The 2019 Stack Overflow Developer Survey Results Are In Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)How to draw graph of this functionWhat is the equation for this graph?What's the graph for this periodic functionWhat is the function that generates this graph?Why can't this be the graph of any function?What is the function behind this graph?What kind of function is represented by this graph?What function created this graph and output?Can this set define the graph of this function?Help me finding function which give this type of graph.

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Why's the Graph of $y = sin (cos (e^x))$ so Wonky?



The 2019 Stack Overflow Developer Survey Results Are In
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)How to draw graph of this functionWhat is the equation for this graph?What's the graph for this periodic functionWhat is the function that generates this graph?Why can't this be the graph of any function?What is the function behind this graph?What kind of function is represented by this graph?What function created this graph and output?Can this set define the graph of this function?Help me finding function which give this type of graph.










1












$begingroup$


I was recently messing around with desmos by plotting random graphs.
I came across this peculiar function, namely $y = sin (cos (e^x))$.
I noticed that the graph is basically a sine wave whose period gets shorter and shorter. However, at a few $x$ values, this trend falters for a bit.
The points I'm referring to are near <span class=$x = 8$, where there are white specks instead of the expected red.">



The points I'm referring to are near $x = 8,$ where there are white specks instead of the expected red. Can someone give me an insight into why this may be happening?



Any help would be greatly appreciated!










share|cite|improve this question











$endgroup$











  • $begingroup$
    Have you also tried plotting the thing you are plugging into $sin$ (i.e. plotting $y=cosleft(e^xright)$)?
    $endgroup$
    – Minus One-Twelfth
    3 hours ago










  • $begingroup$
    @MinusOne-Twelfth How is that supposed to help? It's a function that oscillates faster and faster between $-1$ and $1$, just like this one should oscillate faster and faster between $-sin1$ and $sin1$.
    $endgroup$
    – Saucy O'Path
    3 hours ago










  • $begingroup$
    Maybe by visualising what you're plugging in to sine, you could better visualise the output. Anyway, doesn't hurt to try when exploring this.
    $endgroup$
    – Minus One-Twelfth
    3 hours ago















1












$begingroup$


I was recently messing around with desmos by plotting random graphs.
I came across this peculiar function, namely $y = sin (cos (e^x))$.
I noticed that the graph is basically a sine wave whose period gets shorter and shorter. However, at a few $x$ values, this trend falters for a bit.
The points I'm referring to are near <span class=$x = 8$, where there are white specks instead of the expected red.">



The points I'm referring to are near $x = 8,$ where there are white specks instead of the expected red. Can someone give me an insight into why this may be happening?



Any help would be greatly appreciated!










share|cite|improve this question











$endgroup$











  • $begingroup$
    Have you also tried plotting the thing you are plugging into $sin$ (i.e. plotting $y=cosleft(e^xright)$)?
    $endgroup$
    – Minus One-Twelfth
    3 hours ago










  • $begingroup$
    @MinusOne-Twelfth How is that supposed to help? It's a function that oscillates faster and faster between $-1$ and $1$, just like this one should oscillate faster and faster between $-sin1$ and $sin1$.
    $endgroup$
    – Saucy O'Path
    3 hours ago










  • $begingroup$
    Maybe by visualising what you're plugging in to sine, you could better visualise the output. Anyway, doesn't hurt to try when exploring this.
    $endgroup$
    – Minus One-Twelfth
    3 hours ago













1












1








1





$begingroup$


I was recently messing around with desmos by plotting random graphs.
I came across this peculiar function, namely $y = sin (cos (e^x))$.
I noticed that the graph is basically a sine wave whose period gets shorter and shorter. However, at a few $x$ values, this trend falters for a bit.
The points I'm referring to are near <span class=$x = 8$, where there are white specks instead of the expected red.">



The points I'm referring to are near $x = 8,$ where there are white specks instead of the expected red. Can someone give me an insight into why this may be happening?



Any help would be greatly appreciated!










share|cite|improve this question











$endgroup$




I was recently messing around with desmos by plotting random graphs.
I came across this peculiar function, namely $y = sin (cos (e^x))$.
I noticed that the graph is basically a sine wave whose period gets shorter and shorter. However, at a few $x$ values, this trend falters for a bit.
The points I'm referring to are near <span class=$x = 8$, where there are white specks instead of the expected red.">



The points I'm referring to are near $x = 8,$ where there are white specks instead of the expected red. Can someone give me an insight into why this may be happening?



Any help would be greatly appreciated!







graphing-functions






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited 11 mins ago









YuiTo Cheng

2,40641037




2,40641037










asked 3 hours ago









John A. John A.

301213




301213











  • $begingroup$
    Have you also tried plotting the thing you are plugging into $sin$ (i.e. plotting $y=cosleft(e^xright)$)?
    $endgroup$
    – Minus One-Twelfth
    3 hours ago










  • $begingroup$
    @MinusOne-Twelfth How is that supposed to help? It's a function that oscillates faster and faster between $-1$ and $1$, just like this one should oscillate faster and faster between $-sin1$ and $sin1$.
    $endgroup$
    – Saucy O'Path
    3 hours ago










  • $begingroup$
    Maybe by visualising what you're plugging in to sine, you could better visualise the output. Anyway, doesn't hurt to try when exploring this.
    $endgroup$
    – Minus One-Twelfth
    3 hours ago
















  • $begingroup$
    Have you also tried plotting the thing you are plugging into $sin$ (i.e. plotting $y=cosleft(e^xright)$)?
    $endgroup$
    – Minus One-Twelfth
    3 hours ago










  • $begingroup$
    @MinusOne-Twelfth How is that supposed to help? It's a function that oscillates faster and faster between $-1$ and $1$, just like this one should oscillate faster and faster between $-sin1$ and $sin1$.
    $endgroup$
    – Saucy O'Path
    3 hours ago










  • $begingroup$
    Maybe by visualising what you're plugging in to sine, you could better visualise the output. Anyway, doesn't hurt to try when exploring this.
    $endgroup$
    – Minus One-Twelfth
    3 hours ago















$begingroup$
Have you also tried plotting the thing you are plugging into $sin$ (i.e. plotting $y=cosleft(e^xright)$)?
$endgroup$
– Minus One-Twelfth
3 hours ago




$begingroup$
Have you also tried plotting the thing you are plugging into $sin$ (i.e. plotting $y=cosleft(e^xright)$)?
$endgroup$
– Minus One-Twelfth
3 hours ago












$begingroup$
@MinusOne-Twelfth How is that supposed to help? It's a function that oscillates faster and faster between $-1$ and $1$, just like this one should oscillate faster and faster between $-sin1$ and $sin1$.
$endgroup$
– Saucy O'Path
3 hours ago




$begingroup$
@MinusOne-Twelfth How is that supposed to help? It's a function that oscillates faster and faster between $-1$ and $1$, just like this one should oscillate faster and faster between $-sin1$ and $sin1$.
$endgroup$
– Saucy O'Path
3 hours ago












$begingroup$
Maybe by visualising what you're plugging in to sine, you could better visualise the output. Anyway, doesn't hurt to try when exploring this.
$endgroup$
– Minus One-Twelfth
3 hours ago




$begingroup$
Maybe by visualising what you're plugging in to sine, you could better visualise the output. Anyway, doesn't hurt to try when exploring this.
$endgroup$
– Minus One-Twelfth
3 hours ago










2 Answers
2






active

oldest

votes


















2












$begingroup$

The software may be performing some sampling on $x$ values to plot your function.



When the frequency of your function is low, for this case when $x$ is small, the effect of sampling is not noticeable.



But when the frequency of your function is too high relative to the sampling frequency, precisely when your function's frequency is higher than half the sampling frequency, aliasing occurs and your function is replaced by a lower-frequency function that has the same sample values.



In the extreme case, when the frequency of your function is around a multiple of the sampling frequency, the alias from the samples can appear to be a constant function, a function with lower frequency.



This may give the effect of the missing red around $x=8$, when the displayed frequency of the function is lower than expected.






share|cite|improve this answer









$endgroup$




















    4












    $begingroup$

    That’s simply a rendering error with the software. The graph continues to oscillate as you’d expect. Zoom in and the problem should resolve itself.






    share|cite|improve this answer








    New contributor




    Bruno E is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.






    $endgroup$













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      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      2












      $begingroup$

      The software may be performing some sampling on $x$ values to plot your function.



      When the frequency of your function is low, for this case when $x$ is small, the effect of sampling is not noticeable.



      But when the frequency of your function is too high relative to the sampling frequency, precisely when your function's frequency is higher than half the sampling frequency, aliasing occurs and your function is replaced by a lower-frequency function that has the same sample values.



      In the extreme case, when the frequency of your function is around a multiple of the sampling frequency, the alias from the samples can appear to be a constant function, a function with lower frequency.



      This may give the effect of the missing red around $x=8$, when the displayed frequency of the function is lower than expected.






      share|cite|improve this answer









      $endgroup$

















        2












        $begingroup$

        The software may be performing some sampling on $x$ values to plot your function.



        When the frequency of your function is low, for this case when $x$ is small, the effect of sampling is not noticeable.



        But when the frequency of your function is too high relative to the sampling frequency, precisely when your function's frequency is higher than half the sampling frequency, aliasing occurs and your function is replaced by a lower-frequency function that has the same sample values.



        In the extreme case, when the frequency of your function is around a multiple of the sampling frequency, the alias from the samples can appear to be a constant function, a function with lower frequency.



        This may give the effect of the missing red around $x=8$, when the displayed frequency of the function is lower than expected.






        share|cite|improve this answer









        $endgroup$















          2












          2








          2





          $begingroup$

          The software may be performing some sampling on $x$ values to plot your function.



          When the frequency of your function is low, for this case when $x$ is small, the effect of sampling is not noticeable.



          But when the frequency of your function is too high relative to the sampling frequency, precisely when your function's frequency is higher than half the sampling frequency, aliasing occurs and your function is replaced by a lower-frequency function that has the same sample values.



          In the extreme case, when the frequency of your function is around a multiple of the sampling frequency, the alias from the samples can appear to be a constant function, a function with lower frequency.



          This may give the effect of the missing red around $x=8$, when the displayed frequency of the function is lower than expected.






          share|cite|improve this answer









          $endgroup$



          The software may be performing some sampling on $x$ values to plot your function.



          When the frequency of your function is low, for this case when $x$ is small, the effect of sampling is not noticeable.



          But when the frequency of your function is too high relative to the sampling frequency, precisely when your function's frequency is higher than half the sampling frequency, aliasing occurs and your function is replaced by a lower-frequency function that has the same sample values.



          In the extreme case, when the frequency of your function is around a multiple of the sampling frequency, the alias from the samples can appear to be a constant function, a function with lower frequency.



          This may give the effect of the missing red around $x=8$, when the displayed frequency of the function is lower than expected.







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered 3 hours ago









          peterwhypeterwhy

          12.2k21229




          12.2k21229





















              4












              $begingroup$

              That’s simply a rendering error with the software. The graph continues to oscillate as you’d expect. Zoom in and the problem should resolve itself.






              share|cite|improve this answer








              New contributor




              Bruno E is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
              Check out our Code of Conduct.






              $endgroup$

















                4












                $begingroup$

                That’s simply a rendering error with the software. The graph continues to oscillate as you’d expect. Zoom in and the problem should resolve itself.






                share|cite|improve this answer








                New contributor




                Bruno E is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                Check out our Code of Conduct.






                $endgroup$















                  4












                  4








                  4





                  $begingroup$

                  That’s simply a rendering error with the software. The graph continues to oscillate as you’d expect. Zoom in and the problem should resolve itself.






                  share|cite|improve this answer








                  New contributor




                  Bruno E is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.






                  $endgroup$



                  That’s simply a rendering error with the software. The graph continues to oscillate as you’d expect. Zoom in and the problem should resolve itself.







                  share|cite|improve this answer








                  New contributor




                  Bruno E is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.









                  share|cite|improve this answer



                  share|cite|improve this answer






                  New contributor




                  Bruno E is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.









                  answered 3 hours ago









                  Bruno EBruno E

                  412




                  412




                  New contributor




                  Bruno E is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.





                  New contributor





                  Bruno E is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.






                  Bruno E is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.



























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                      ValueError: Expected n_neighbors <= n_samples, but n_samples = 1, n_neighbors = 6 (SMOTE) The 2019 Stack Overflow Developer Survey Results Are InCan SMOTE be applied over sequence of words (sentences)?ValueError when doing validation with random forestsSMOTE and multi class oversamplingLogic behind SMOTE-NC?ValueError: Error when checking target: expected dense_1 to have shape (7,) but got array with shape (1,)SmoteBoost: Should SMOTE be ran individually for each iteration/tree in the boosting?solving multi-class imbalance classification using smote and OSSUsing SMOTE for Synthetic Data generation to improve performance on unbalanced dataproblem of entry format for a simple model in KerasSVM SMOTE fit_resample() function runs forever with no result