Newton's cubic curve

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











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https://www.theguardian.com/science/alexs-adventures-in-numberland/2017/may/01/the-colour-of-numbers-visions-of-our-mathematical-universe



is written that Isaac Newton has investigated properties of the curve x^3 – abx + a^3 – cy^2 = 0, where a, b and c are constants. The image above is the curve of this equation when a = 1, c = 4 and b ranges from –8 to 8.
The image seems to me extremely aesthetic, almost artistic work. I'd have image on the wall like a poster, but with



ContourPlot[
 Evaluate@Table[x^3 + b x == 4 y^2, b, -8, 8, 1], x, -5, 
 5, y, -5, 5, Frame -> None, ImageSize -> 600, 
 ContourStyle -> Black, PlotPoints -> 20]


I can not reproduce that image, the result is a bit different. Can someone please explain, what is wrong with my code? Regards, Darko






plotting







share|improve this question







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















  • 2




    Well, you seem to have done your substitutions incorrectly. The correct equation you should plot is x^3 - b x - 4 y^2 + 1 == 0. You are missing a constant, and the b x term seems to have the wrong sign. If you change the equation to the one I showed, the plots is much more similar to the one in the link. You might also want to restrict the range of x to e.g. x, -5, 3.5.
    – MarcoB
    2 hours ago











  • I'm sorry, I do not know how I managed to make such a ridiculous mistake.
    – Darko G
    1 hour ago














up vote
2
down vote

favorite












In article



https://www.theguardian.com/science/alexs-adventures-in-numberland/2017/may/01/the-colour-of-numbers-visions-of-our-mathematical-universe



is written that Isaac Newton has investigated properties of the curve x^3 – abx + a^3 – cy^2 = 0, where a, b and c are constants. The image above is the curve of this equation when a = 1, c = 4 and b ranges from –8 to 8.
The image seems to me extremely aesthetic, almost artistic work. I'd have image on the wall like a poster, but with



ContourPlot[
 Evaluate@Table[x^3 + b x == 4 y^2, b, -8, 8, 1], x, -5, 
 5, y, -5, 5, Frame -> None, ImageSize -> 600, 
 ContourStyle -> Black, PlotPoints -> 20]


I can not reproduce that image, the result is a bit different. Can someone please explain, what is wrong with my code? Regards, Darko






plotting







share|improve this question







New contributor




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















  • 2




    Well, you seem to have done your substitutions incorrectly. The correct equation you should plot is x^3 - b x - 4 y^2 + 1 == 0. You are missing a constant, and the b x term seems to have the wrong sign. If you change the equation to the one I showed, the plots is much more similar to the one in the link. You might also want to restrict the range of x to e.g. x, -5, 3.5.
    – MarcoB
    2 hours ago











  • I'm sorry, I do not know how I managed to make such a ridiculous mistake.
    – Darko G
    1 hour ago












up vote
2
down vote

favorite









up vote
2
down vote

favorite











In article



https://www.theguardian.com/science/alexs-adventures-in-numberland/2017/may/01/the-colour-of-numbers-visions-of-our-mathematical-universe



is written that Isaac Newton has investigated properties of the curve x^3 – abx + a^3 – cy^2 = 0, where a, b and c are constants. The image above is the curve of this equation when a = 1, c = 4 and b ranges from –8 to 8.
The image seems to me extremely aesthetic, almost artistic work. I'd have image on the wall like a poster, but with



ContourPlot[
 Evaluate@Table[x^3 + b x == 4 y^2, b, -8, 8, 1], x, -5, 
 5, y, -5, 5, Frame -> None, ImageSize -> 600, 
 ContourStyle -> Black, PlotPoints -> 20]


I can not reproduce that image, the result is a bit different. Can someone please explain, what is wrong with my code? Regards, Darko






plotting







share|improve this question







New contributor




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











In article



https://www.theguardian.com/science/alexs-adventures-in-numberland/2017/may/01/the-colour-of-numbers-visions-of-our-mathematical-universe



is written that Isaac Newton has investigated properties of the curve x^3 – abx + a^3 – cy^2 = 0, where a, b and c are constants. The image above is the curve of this equation when a = 1, c = 4 and b ranges from –8 to 8.
The image seems to me extremely aesthetic, almost artistic work. I'd have image on the wall like a poster, but with



ContourPlot[
 Evaluate@Table[x^3 + b x == 4 y^2, b, -8, 8, 1], x, -5, 
 5, y, -5, 5, Frame -> None, ImageSize -> 600, 
 ContourStyle -> Black, PlotPoints -> 20]


I can not reproduce that image, the result is a bit different. Can someone please explain, what is wrong with my code? Regards, Darko






plotting




plotting






share|improve this question







New contributor




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











share|improve this question







New contributor




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









share|improve this question




share|improve this question






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Darko G

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Check out our Code of Conduct.







  • 2




    Well, you seem to have done your substitutions incorrectly. The correct equation you should plot is x^3 - b x - 4 y^2 + 1 == 0. You are missing a constant, and the b x term seems to have the wrong sign. If you change the equation to the one I showed, the plots is much more similar to the one in the link. You might also want to restrict the range of x to e.g. x, -5, 3.5.
    – MarcoB
    2 hours ago











  • I'm sorry, I do not know how I managed to make such a ridiculous mistake.
    – Darko G
    1 hour ago












  • 2




    Well, you seem to have done your substitutions incorrectly. The correct equation you should plot is x^3 - b x - 4 y^2 + 1 == 0. You are missing a constant, and the b x term seems to have the wrong sign. If you change the equation to the one I showed, the plots is much more similar to the one in the link. You might also want to restrict the range of x to e.g. x, -5, 3.5.
    – MarcoB
    2 hours ago











  • I'm sorry, I do not know how I managed to make such a ridiculous mistake.
    – Darko G
    1 hour ago







2




2




Well, you seem to have done your substitutions incorrectly. The correct equation you should plot is x^3 - b x - 4 y^2 + 1 == 0. You are missing a constant, and the b x term seems to have the wrong sign. If you change the equation to the one I showed, the plots is much more similar to the one in the link. You might also want to restrict the range of x to e.g. x, -5, 3.5.
– MarcoB
2 hours ago





Well, you seem to have done your substitutions incorrectly. The correct equation you should plot is x^3 - b x - 4 y^2 + 1 == 0. You are missing a constant, and the b x term seems to have the wrong sign. If you change the equation to the one I showed, the plots is much more similar to the one in the link. You might also want to restrict the range of x to e.g. x, -5, 3.5.
– MarcoB
2 hours ago













I'm sorry, I do not know how I managed to make such a ridiculous mistake.
– Darko G
1 hour ago




I'm sorry, I do not know how I managed to make such a ridiculous mistake.
– Darko G
1 hour ago










1 Answer
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4
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You are plotting wrong equation, See this. 



a = 1; c = 4;
ContourPlot[
Evaluate@Table[x^3 - a*b *x + a^3 - c*y^2 == 0, b, -8, 8, 0.5], x, -3., 
3., y, -3.5, 3.5, Frame -> None, ImageSize -> 600, 
ContourStyle -> Directive[Thickness[0.0015],PlotPoints -> 20]


I have changed the step size of $b$ and plot range of axis to mimic with the figure in that link.



It plots as:
enter image description here






share|improve this answer


















  • 1




    You can maintain sharpness while increasing the number of steps (b, -8, 8, 1/2) by using ContourStyle -> Directive[Thin, Black]
    – Bob Hanlon
    1 hour ago










  • @BobHanlon, Modified, Thank you
    – Sachin Kumar
    5 mins ago










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1 Answer
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active

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1 Answer
1






active

oldest

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active

oldest

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active

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up vote
4
down vote













You are plotting wrong equation, See this. 



a = 1; c = 4;
ContourPlot[
Evaluate@Table[x^3 - a*b *x + a^3 - c*y^2 == 0, b, -8, 8, 0.5], x, -3., 
3., y, -3.5, 3.5, Frame -> None, ImageSize -> 600, 
ContourStyle -> Directive[Thickness[0.0015],PlotPoints -> 20]


I have changed the step size of $b$ and plot range of axis to mimic with the figure in that link.



It plots as:
enter image description here






share|improve this answer


















  • 1




    You can maintain sharpness while increasing the number of steps (b, -8, 8, 1/2) by using ContourStyle -> Directive[Thin, Black]
    – Bob Hanlon
    1 hour ago










  • @BobHanlon, Modified, Thank you
    – Sachin Kumar
    5 mins ago














up vote
4
down vote













You are plotting wrong equation, See this. 



a = 1; c = 4;
ContourPlot[
Evaluate@Table[x^3 - a*b *x + a^3 - c*y^2 == 0, b, -8, 8, 0.5], x, -3., 
3., y, -3.5, 3.5, Frame -> None, ImageSize -> 600, 
ContourStyle -> Directive[Thickness[0.0015],PlotPoints -> 20]


I have changed the step size of $b$ and plot range of axis to mimic with the figure in that link.



It plots as:
enter image description here






share|improve this answer


















  • 1




    You can maintain sharpness while increasing the number of steps (b, -8, 8, 1/2) by using ContourStyle -> Directive[Thin, Black]
    – Bob Hanlon
    1 hour ago










  • @BobHanlon, Modified, Thank you
    – Sachin Kumar
    5 mins ago












up vote
4
down vote










up vote
4
down vote









You are plotting wrong equation, See this. 



a = 1; c = 4;
ContourPlot[
Evaluate@Table[x^3 - a*b *x + a^3 - c*y^2 == 0, b, -8, 8, 0.5], x, -3., 
3., y, -3.5, 3.5, Frame -> None, ImageSize -> 600, 
ContourStyle -> Directive[Thickness[0.0015],PlotPoints -> 20]


I have changed the step size of $b$ and plot range of axis to mimic with the figure in that link.



It plots as:
enter image description here






share|improve this answer














You are plotting wrong equation, See this. 



a = 1; c = 4;
ContourPlot[
Evaluate@Table[x^3 - a*b *x + a^3 - c*y^2 == 0, b, -8, 8, 0.5], x, -3., 
3., y, -3.5, 3.5, Frame -> None, ImageSize -> 600, 
ContourStyle -> Directive[Thickness[0.0015],PlotPoints -> 20]


I have changed the step size of $b$ and plot range of axis to mimic with the figure in that link.



It plots as:
enter image description here







share|improve this answer














share|improve this answer



share|improve this answer








edited 7 mins ago

























answered 2 hours ago









Sachin Kumar

1427




1427







  • 1




    You can maintain sharpness while increasing the number of steps (b, -8, 8, 1/2) by using ContourStyle -> Directive[Thin, Black]
    – Bob Hanlon
    1 hour ago










  • @BobHanlon, Modified, Thank you
    – Sachin Kumar
    5 mins ago












  • 1




    You can maintain sharpness while increasing the number of steps (b, -8, 8, 1/2) by using ContourStyle -> Directive[Thin, Black]
    – Bob Hanlon
    1 hour ago










  • @BobHanlon, Modified, Thank you
    – Sachin Kumar
    5 mins ago







1




1




You can maintain sharpness while increasing the number of steps (b, -8, 8, 1/2) by using ContourStyle -> Directive[Thin, Black]
– Bob Hanlon
1 hour ago




You can maintain sharpness while increasing the number of steps (b, -8, 8, 1/2) by using ContourStyle -> Directive[Thin, Black]
– Bob Hanlon
1 hour ago












@BobHanlon, Modified, Thank you
– Sachin Kumar
5 mins ago




@BobHanlon, Modified, Thank you
– Sachin Kumar
5 mins ago










Darko G is a new contributor. Be nice, and check out our Code of Conduct.









 

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