How to plot complex functions on the paper by your hand?
I want to know the exact method of plotting complex function used by human, computer, and whatever who can do mathematics.
For example how should I plot this : $w = u+iv$ , $z = x+iy$ , $w= f(z)= z^2$
I'm completely confused imagining the complex functions and I want to know how you would imagine such functions and do mathematics with it.
Thanks in advance
complex-analysis graphing-functions
edited Dec 28 '13 at 19:46
mathematics2x2life
8,04221738
asked Dec 28 '13 at 19:45
FreeMind
9071133
|
show 5 more comments
I want to know the exact method of plotting complex function used by human, computer, and whatever who can do mathematics.
For example how should I plot this : $w = u+iv$ , $z = x+iy$ , $w= f(z)= z^2$
I'm completely confused imagining the complex functions and I want to know how you would imagine such functions and do mathematics with it.
Thanks in advance
complex-analysis graphing-functions
edited Dec 28 '13 at 19:46
mathematics2x2life
8,04221738
asked Dec 28 '13 at 19:45
FreeMind
9071133
Do you understand that you can't plot functions from $mathbb R^2$ to $mathbb R^2$?
– Git Gud
Dec 28 '13 at 19:47
No, you mean it's not possible to plot such function?
– FreeMind
Dec 28 '13 at 19:47
Yes, it isn't possible to plot such functions in the traditional sense of 'plot'.
– Git Gud
Dec 28 '13 at 19:49
you're confused by not precisely defining, what you have and what you want.
– V-X
Dec 28 '13 at 19:49
2
@MrWho You can't plot from $mathbb R^2$ to $mathbb R^2$ for the reason mathematics2x2life gives in his answer. See this link for a different way of plotting functions.
– Git Gud
Dec 28 '13 at 19:53
|
show 5 more comments
I want to know the exact method of plotting complex function used by human, computer, and whatever who can do mathematics.
For example how should I plot this : $w = u+iv$ , $z = x+iy$ , $w= f(z)= z^2$
I'm completely confused imagining the complex functions and I want to know how you would imagine such functions and do mathematics with it.
Thanks in advance
complex-analysis graphing-functions
edited Dec 28 '13 at 19:46
mathematics2x2life
8,04221738
asked Dec 28 '13 at 19:45
FreeMind
9071133
I want to know the exact method of plotting complex function used by human, computer, and whatever who can do mathematics.
For example how should I plot this : $w = u+iv$ , $z = x+iy$ , $w= f(z)= z^2$
I'm completely confused imagining the complex functions and I want to know how you would imagine such functions and do mathematics with it.
Thanks in advance
complex-analysis graphing-functions
complex-analysis graphing-functions
edited Dec 28 '13 at 19:46
mathematics2x2life
8,04221738
asked Dec 28 '13 at 19:45
FreeMind
9071133
edited Dec 28 '13 at 19:46
mathematics2x2life
8,04221738
asked Dec 28 '13 at 19:45
FreeMind
9071133
edited Dec 28 '13 at 19:46
mathematics2x2life
8,04221738
edited Dec 28 '13 at 19:46
mathematics2x2life
8,04221738
edited Dec 28 '13 at 19:46
mathematics2x2life
8,04221738
8,04221738
asked Dec 28 '13 at 19:45
FreeMind
9071133
asked Dec 28 '13 at 19:45
FreeMind
9071133
asked Dec 28 '13 at 19:45
FreeMind
9071133
9071133
Do you understand that you can't plot functions from $mathbb R^2$ to $mathbb R^2$?
– Git Gud
Dec 28 '13 at 19:47
No, you mean it's not possible to plot such function?
– FreeMind
Dec 28 '13 at 19:47
Yes, it isn't possible to plot such functions in the traditional sense of 'plot'.
– Git Gud
Dec 28 '13 at 19:49
you're confused by not precisely defining, what you have and what you want.
– V-X
Dec 28 '13 at 19:49
2
@MrWho You can't plot from $mathbb R^2$ to $mathbb R^2$ for the reason mathematics2x2life gives in his answer. See this link for a different way of plotting functions.
– Git Gud
Dec 28 '13 at 19:53
|
show 5 more comments
Do you understand that you can't plot functions from $mathbb R^2$ to $mathbb R^2$?
– Git Gud
Dec 28 '13 at 19:47
No, you mean it's not possible to plot such function?
– FreeMind
Dec 28 '13 at 19:47
Yes, it isn't possible to plot such functions in the traditional sense of 'plot'.
– Git Gud
Dec 28 '13 at 19:49
you're confused by not precisely defining, what you have and what you want.
– V-X
Dec 28 '13 at 19:49
2
@MrWho You can't plot from $mathbb R^2$ to $mathbb R^2$ for the reason mathematics2x2life gives in his answer. See this link for a different way of plotting functions.
– Git Gud
Dec 28 '13 at 19:53
Do you understand that you can't plot functions from $mathbb R^2$ to $mathbb R^2$?
– Git Gud
Dec 28 '13 at 19:47
Do you understand that you can't plot functions from $mathbb R^2$ to $mathbb R^2$?
– Git Gud
Dec 28 '13 at 19:47
No, you mean it's not possible to plot such function?
– FreeMind
Dec 28 '13 at 19:47
No, you mean it's not possible to plot such function?
– FreeMind
Dec 28 '13 at 19:47
Yes, it isn't possible to plot such functions in the traditional sense of 'plot'.
– Git Gud
Dec 28 '13 at 19:49
Yes, it isn't possible to plot such functions in the traditional sense of 'plot'.
– Git Gud
Dec 28 '13 at 19:49
you're confused by not precisely defining, what you have and what you want.
– V-X
Dec 28 '13 at 19:49
you're confused by not precisely defining, what you have and what you want.
– V-X
Dec 28 '13 at 19:49
2
2
@MrWho You can't plot from $mathbb R^2$ to $mathbb R^2$ for the reason mathematics2x2life gives in his answer. See this link for a different way of plotting functions.
– Git Gud
Dec 28 '13 at 19:53
@MrWho You can't plot from $mathbb R^2$ to $mathbb R^2$ for the reason mathematics2x2life gives in his answer. See this link for a different way of plotting functions.
– Git Gud
Dec 28 '13 at 19:53
|
show 5 more comments
3 Answers
3
active
oldest
votes
You don't plot these. To plot them would require $2$ axes to plot the real and imaginary components of the inputs and they it would require another $2$ axes to plot the real and imaginary components of the outputs, totaling $4$ axes. However, we are unable to plot in $4$-dimensions in our $3$ dimensional world. So we must make a choice: plot the imaginary part of the output or the real part of the output. For example, take the function $f(z)=z^2$. Then we have
$$
f(2+i)=(2+i)^2=4+4i-1=3+4i
$$
We could then plot the imaginary part of the output, $4i$. So this would be the same as plotting the point $(2,1,4)$ in $mathbb{R}^3$.
NOTE. This isn't the only thing we could plot. For example, another common choice is to plot the absolute value of the output. In our example above, we would have $f(2+i)=3+4i$. Then we know that $|3+4i|=sqrt{25}=5$. So we would plot the point $(2,1,5)$. It all depends on the choice of the final variable to plot while the $2$ first axes are almost always the real and imaginary components of the input, respectively.
answered Dec 28 '13 at 19:50
mathematics2x2life
8,04221738
What's the problem? Couldn't we plot (2,1,4) in the R^3?!
– FreeMind
Dec 28 '13 at 19:55
Yes, we could and we do. That's the point. We can plot that but we cannot plot the point $(2,1,3,4)$ which would be needed to properly visualize the output of $f(2+i)$ in my example.
– mathematics2x2life
Dec 28 '13 at 19:57
Plotting complex function is still hard for me to grasp!
– FreeMind
Dec 31 '13 at 21:01
2
It should be given that it is humanly impossible to do as it needs to be done, as I explained. Moreover, it's not that important in Complex Analysis as even if we do plot, it is a computer program that does the work for us. More important to learn the theory like the Cauchy-Goursat Theorem, Residue Theorem, Cauchy Integral Formula, etc.
– mathematics2x2life
Dec 31 '13 at 23:23
However, I want to have geometric imagination of what I'm really doing, if you know any article or something which has explained plotting clearly please let me know.
– FreeMind
Jan 1 '14 at 10:31
|
show 1 more comment
You can plot such functions! Look at https://people.math.osu.edu/fowler.291/phase/
for instance. The color at a point tells you the phase of the image of that point. To see what the base "phase chart" is, just plot the identity function $z$.
If you wanted phase and modulus info, you could do a 3D plot colored by phase. I did that too using webGL and cannot find it now. Will update this later when I do...
answered Dec 28 '13 at 20:08
Steven Gubkin
5,5741531
add a comment |
Like Steven Gubkin says, coloring by phase can give you excellent geometric intuitions. I put together this Python code while I was taking complex analysis, let me know what you think: https://github.com/seaplant3/complex-plotting
It uses contours (like an elevation map) to show magnitude, I found that was the easiest way to keep everything visible.
answered Jan 22 at 7:03
seaplant
92
While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review
– TheSimpliFire
Jan 22 at 7:49
What 'essential parts of the answer' are missing?
– seaplant
Jan 22 at 8:12
Your relevant Python code, in case the link changes/goes down.
– TheSimpliFire
Jan 22 at 18:51
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
You don't plot these. To plot them would require $2$ axes to plot the real and imaginary components of the inputs and they it would require another $2$ axes to plot the real and imaginary components of the outputs, totaling $4$ axes. However, we are unable to plot in $4$-dimensions in our $3$ dimensional world. So we must make a choice: plot the imaginary part of the output or the real part of the output. For example, take the function $f(z)=z^2$. Then we have
$$
f(2+i)=(2+i)^2=4+4i-1=3+4i
$$
We could then plot the imaginary part of the output, $4i$. So this would be the same as plotting the point $(2,1,4)$ in $mathbb{R}^3$.
NOTE. This isn't the only thing we could plot. For example, another common choice is to plot the absolute value of the output. In our example above, we would have $f(2+i)=3+4i$. Then we know that $|3+4i|=sqrt{25}=5$. So we would plot the point $(2,1,5)$. It all depends on the choice of the final variable to plot while the $2$ first axes are almost always the real and imaginary components of the input, respectively.
answered Dec 28 '13 at 19:50
mathematics2x2life
8,04221738
What's the problem? Couldn't we plot (2,1,4) in the R^3?!
– FreeMind
Dec 28 '13 at 19:55
Yes, we could and we do. That's the point. We can plot that but we cannot plot the point $(2,1,3,4)$ which would be needed to properly visualize the output of $f(2+i)$ in my example.
– mathematics2x2life
Dec 28 '13 at 19:57
Plotting complex function is still hard for me to grasp!
– FreeMind
Dec 31 '13 at 21:01
2
It should be given that it is humanly impossible to do as it needs to be done, as I explained. Moreover, it's not that important in Complex Analysis as even if we do plot, it is a computer program that does the work for us. More important to learn the theory like the Cauchy-Goursat Theorem, Residue Theorem, Cauchy Integral Formula, etc.
– mathematics2x2life
Dec 31 '13 at 23:23
However, I want to have geometric imagination of what I'm really doing, if you know any article or something which has explained plotting clearly please let me know.
– FreeMind
Jan 1 '14 at 10:31
|
show 1 more comment
You don't plot these. To plot them would require $2$ axes to plot the real and imaginary components of the inputs and they it would require another $2$ axes to plot the real and imaginary components of the outputs, totaling $4$ axes. However, we are unable to plot in $4$-dimensions in our $3$ dimensional world. So we must make a choice: plot the imaginary part of the output or the real part of the output. For example, take the function $f(z)=z^2$. Then we have
$$
f(2+i)=(2+i)^2=4+4i-1=3+4i
$$
We could then plot the imaginary part of the output, $4i$. So this would be the same as plotting the point $(2,1,4)$ in $mathbb{R}^3$.
NOTE. This isn't the only thing we could plot. For example, another common choice is to plot the absolute value of the output. In our example above, we would have $f(2+i)=3+4i$. Then we know that $|3+4i|=sqrt{25}=5$. So we would plot the point $(2,1,5)$. It all depends on the choice of the final variable to plot while the $2$ first axes are almost always the real and imaginary components of the input, respectively.
answered Dec 28 '13 at 19:50
mathematics2x2life
8,04221738
What's the problem? Couldn't we plot (2,1,4) in the R^3?!
– FreeMind
Dec 28 '13 at 19:55
Yes, we could and we do. That's the point. We can plot that but we cannot plot the point $(2,1,3,4)$ which would be needed to properly visualize the output of $f(2+i)$ in my example.
– mathematics2x2life
Dec 28 '13 at 19:57
Plotting complex function is still hard for me to grasp!
– FreeMind
Dec 31 '13 at 21:01
2
It should be given that it is humanly impossible to do as it needs to be done, as I explained. Moreover, it's not that important in Complex Analysis as even if we do plot, it is a computer program that does the work for us. More important to learn the theory like the Cauchy-Goursat Theorem, Residue Theorem, Cauchy Integral Formula, etc.
– mathematics2x2life
Dec 31 '13 at 23:23
However, I want to have geometric imagination of what I'm really doing, if you know any article or something which has explained plotting clearly please let me know.
– FreeMind
Jan 1 '14 at 10:31
|
show 1 more comment
You don't plot these. To plot them would require $2$ axes to plot the real and imaginary components of the inputs and they it would require another $2$ axes to plot the real and imaginary components of the outputs, totaling $4$ axes. However, we are unable to plot in $4$-dimensions in our $3$ dimensional world. So we must make a choice: plot the imaginary part of the output or the real part of the output. For example, take the function $f(z)=z^2$. Then we have
$$
f(2+i)=(2+i)^2=4+4i-1=3+4i
$$
We could then plot the imaginary part of the output, $4i$. So this would be the same as plotting the point $(2,1,4)$ in $mathbb{R}^3$.
NOTE. This isn't the only thing we could plot. For example, another common choice is to plot the absolute value of the output. In our example above, we would have $f(2+i)=3+4i$. Then we know that $|3+4i|=sqrt{25}=5$. So we would plot the point $(2,1,5)$. It all depends on the choice of the final variable to plot while the $2$ first axes are almost always the real and imaginary components of the input, respectively.
answered Dec 28 '13 at 19:50
mathematics2x2life
8,04221738
You don't plot these. To plot them would require $2$ axes to plot the real and imaginary components of the inputs and they it would require another $2$ axes to plot the real and imaginary components of the outputs, totaling $4$ axes. However, we are unable to plot in $4$-dimensions in our $3$ dimensional world. So we must make a choice: plot the imaginary part of the output or the real part of the output. For example, take the function $f(z)=z^2$. Then we have
$$
f(2+i)=(2+i)^2=4+4i-1=3+4i
$$
We could then plot the imaginary part of the output, $4i$. So this would be the same as plotting the point $(2,1,4)$ in $mathbb{R}^3$.
NOTE. This isn't the only thing we could plot. For example, another common choice is to plot the absolute value of the output. In our example above, we would have $f(2+i)=3+4i$. Then we know that $|3+4i|=sqrt{25}=5$. So we would plot the point $(2,1,5)$. It all depends on the choice of the final variable to plot while the $2$ first axes are almost always the real and imaginary components of the input, respectively.
answered Dec 28 '13 at 19:50
mathematics2x2life
8,04221738
edited Dec 28 '13 at 19:56
answered Dec 28 '13 at 19:50
mathematics2x2life
8,04221738
answered Dec 28 '13 at 19:50
mathematics2x2life
8,04221738
answered Dec 28 '13 at 19:50
mathematics2x2life
8,04221738
8,04221738
What's the problem? Couldn't we plot (2,1,4) in the R^3?!
– FreeMind
Dec 28 '13 at 19:55
Yes, we could and we do. That's the point. We can plot that but we cannot plot the point $(2,1,3,4)$ which would be needed to properly visualize the output of $f(2+i)$ in my example.
– mathematics2x2life
Dec 28 '13 at 19:57
Plotting complex function is still hard for me to grasp!
– FreeMind
Dec 31 '13 at 21:01
2
It should be given that it is humanly impossible to do as it needs to be done, as I explained. Moreover, it's not that important in Complex Analysis as even if we do plot, it is a computer program that does the work for us. More important to learn the theory like the Cauchy-Goursat Theorem, Residue Theorem, Cauchy Integral Formula, etc.
– mathematics2x2life
Dec 31 '13 at 23:23
However, I want to have geometric imagination of what I'm really doing, if you know any article or something which has explained plotting clearly please let me know.
– FreeMind
Jan 1 '14 at 10:31
|
show 1 more comment
What's the problem? Couldn't we plot (2,1,4) in the R^3?!
– FreeMind
Dec 28 '13 at 19:55
Yes, we could and we do. That's the point. We can plot that but we cannot plot the point $(2,1,3,4)$ which would be needed to properly visualize the output of $f(2+i)$ in my example.
– mathematics2x2life
Dec 28 '13 at 19:57
Plotting complex function is still hard for me to grasp!
– FreeMind
Dec 31 '13 at 21:01
2
It should be given that it is humanly impossible to do as it needs to be done, as I explained. Moreover, it's not that important in Complex Analysis as even if we do plot, it is a computer program that does the work for us. More important to learn the theory like the Cauchy-Goursat Theorem, Residue Theorem, Cauchy Integral Formula, etc.
– mathematics2x2life
Dec 31 '13 at 23:23
However, I want to have geometric imagination of what I'm really doing, if you know any article or something which has explained plotting clearly please let me know.
– FreeMind
Jan 1 '14 at 10:31
What's the problem? Couldn't we plot (2,1,4) in the R^3?!
– FreeMind
Dec 28 '13 at 19:55
What's the problem? Couldn't we plot (2,1,4) in the R^3?!
– FreeMind
Dec 28 '13 at 19:55
Yes, we could and we do. That's the point. We can plot that but we cannot plot the point $(2,1,3,4)$ which would be needed to properly visualize the output of $f(2+i)$ in my example.
– mathematics2x2life
Dec 28 '13 at 19:57
Yes, we could and we do. That's the point. We can plot that but we cannot plot the point $(2,1,3,4)$ which would be needed to properly visualize the output of $f(2+i)$ in my example.
– mathematics2x2life
Dec 28 '13 at 19:57
Plotting complex function is still hard for me to grasp!
– FreeMind
Dec 31 '13 at 21:01
Plotting complex function is still hard for me to grasp!
– FreeMind
Dec 31 '13 at 21:01
2
2
It should be given that it is humanly impossible to do as it needs to be done, as I explained. Moreover, it's not that important in Complex Analysis as even if we do plot, it is a computer program that does the work for us. More important to learn the theory like the Cauchy-Goursat Theorem, Residue Theorem, Cauchy Integral Formula, etc.
– mathematics2x2life
Dec 31 '13 at 23:23
It should be given that it is humanly impossible to do as it needs to be done, as I explained. Moreover, it's not that important in Complex Analysis as even if we do plot, it is a computer program that does the work for us. More important to learn the theory like the Cauchy-Goursat Theorem, Residue Theorem, Cauchy Integral Formula, etc.
– mathematics2x2life
Dec 31 '13 at 23:23
However, I want to have geometric imagination of what I'm really doing, if you know any article or something which has explained plotting clearly please let me know.
– FreeMind
Jan 1 '14 at 10:31
However, I want to have geometric imagination of what I'm really doing, if you know any article or something which has explained plotting clearly please let me know.
– FreeMind
Jan 1 '14 at 10:31
|
show 1 more comment
You can plot such functions! Look at https://people.math.osu.edu/fowler.291/phase/
for instance. The color at a point tells you the phase of the image of that point. To see what the base "phase chart" is, just plot the identity function $z$.
If you wanted phase and modulus info, you could do a 3D plot colored by phase. I did that too using webGL and cannot find it now. Will update this later when I do...
answered Dec 28 '13 at 20:08
Steven Gubkin
5,5741531
add a comment |
You can plot such functions! Look at https://people.math.osu.edu/fowler.291/phase/
for instance. The color at a point tells you the phase of the image of that point. To see what the base "phase chart" is, just plot the identity function $z$.
If you wanted phase and modulus info, you could do a 3D plot colored by phase. I did that too using webGL and cannot find it now. Will update this later when I do...
answered Dec 28 '13 at 20:08
Steven Gubkin
5,5741531
add a comment |
You can plot such functions! Look at https://people.math.osu.edu/fowler.291/phase/
for instance. The color at a point tells you the phase of the image of that point. To see what the base "phase chart" is, just plot the identity function $z$.
If you wanted phase and modulus info, you could do a 3D plot colored by phase. I did that too using webGL and cannot find it now. Will update this later when I do...
answered Dec 28 '13 at 20:08
Steven Gubkin
5,5741531
You can plot such functions! Look at https://people.math.osu.edu/fowler.291/phase/
for instance. The color at a point tells you the phase of the image of that point. To see what the base "phase chart" is, just plot the identity function $z$.
If you wanted phase and modulus info, you could do a 3D plot colored by phase. I did that too using webGL and cannot find it now. Will update this later when I do...
answered Dec 28 '13 at 20:08
Steven Gubkin
5,5741531
answered Dec 28 '13 at 20:08
Steven Gubkin
5,5741531
answered Dec 28 '13 at 20:08
Steven Gubkin
5,5741531
answered Dec 28 '13 at 20:08
Steven Gubkin
5,5741531
5,5741531
add a comment |
add a comment |
Like Steven Gubkin says, coloring by phase can give you excellent geometric intuitions. I put together this Python code while I was taking complex analysis, let me know what you think: https://github.com/seaplant3/complex-plotting
It uses contours (like an elevation map) to show magnitude, I found that was the easiest way to keep everything visible.
answered Jan 22 at 7:03
seaplant
92
While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review
– TheSimpliFire
Jan 22 at 7:49
What 'essential parts of the answer' are missing?
– seaplant
Jan 22 at 8:12
Your relevant Python code, in case the link changes/goes down.
– TheSimpliFire
Jan 22 at 18:51
add a comment |
Like Steven Gubkin says, coloring by phase can give you excellent geometric intuitions. I put together this Python code while I was taking complex analysis, let me know what you think: https://github.com/seaplant3/complex-plotting
It uses contours (like an elevation map) to show magnitude, I found that was the easiest way to keep everything visible.
answered Jan 22 at 7:03
seaplant
92
While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review
– TheSimpliFire
Jan 22 at 7:49
What 'essential parts of the answer' are missing?
– seaplant
Jan 22 at 8:12
Your relevant Python code, in case the link changes/goes down.
– TheSimpliFire
Jan 22 at 18:51
add a comment |
Like Steven Gubkin says, coloring by phase can give you excellent geometric intuitions. I put together this Python code while I was taking complex analysis, let me know what you think: https://github.com/seaplant3/complex-plotting
It uses contours (like an elevation map) to show magnitude, I found that was the easiest way to keep everything visible.
answered Jan 22 at 7:03
seaplant
92
Like Steven Gubkin says, coloring by phase can give you excellent geometric intuitions. I put together this Python code while I was taking complex analysis, let me know what you think: https://github.com/seaplant3/complex-plotting
It uses contours (like an elevation map) to show magnitude, I found that was the easiest way to keep everything visible.
answered Jan 22 at 7:03
seaplant
92
answered Jan 22 at 7:03
seaplant
92
answered Jan 22 at 7:03
seaplant
92
answered Jan 22 at 7:03
seaplant
92
92
While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review
– TheSimpliFire
Jan 22 at 7:49
What 'essential parts of the answer' are missing?
– seaplant
Jan 22 at 8:12
Your relevant Python code, in case the link changes/goes down.
– TheSimpliFire
Jan 22 at 18:51
add a comment |
While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review
– TheSimpliFire
Jan 22 at 7:49
What 'essential parts of the answer' are missing?
– seaplant
Jan 22 at 8:12
Your relevant Python code, in case the link changes/goes down.
– TheSimpliFire
Jan 22 at 18:51
While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review
– TheSimpliFire
Jan 22 at 7:49
While this link may answer the question, it is better to include the essential parts of the answer here and provide the link for reference. Link-only answers can become invalid if the linked page changes. - From Review
– TheSimpliFire
Jan 22 at 7:49
What 'essential parts of the answer' are missing?
– seaplant
Jan 22 at 8:12
What 'essential parts of the answer' are missing?
– seaplant
Jan 22 at 8:12
Your relevant Python code, in case the link changes/goes down.
– TheSimpliFire
Jan 22 at 18:51
Your relevant Python code, in case the link changes/goes down.
– TheSimpliFire
Jan 22 at 18:51
add a comment |
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Do you understand that you can't plot functions from $mathbb R^2$ to $mathbb R^2$?
– Git Gud
Dec 28 '13 at 19:47
No, you mean it's not possible to plot such function?
– FreeMind
Dec 28 '13 at 19:47
Yes, it isn't possible to plot such functions in the traditional sense of 'plot'.
– Git Gud
Dec 28 '13 at 19:49
you're confused by not precisely defining, what you have and what you want.
– V-X
Dec 28 '13 at 19:49
2
@MrWho You can't plot from $mathbb R^2$ to $mathbb R^2$ for the reason mathematics2x2life gives in his answer. See this link for a different way of plotting functions.
– Git Gud
Dec 28 '13 at 19:53