Newton's cubic curve

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This article from The Guardian discusses Isaac Newton's investigation of the 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 seemsextremely aesthetic to me , 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?






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.
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  • 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
    10 hours ago











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














up vote
5
down vote

favorite












This article from The Guardian discusses Isaac Newton's investigation of the 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 seemsextremely aesthetic to me , 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?






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
    10 hours ago











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












up vote
5
down vote

favorite









up vote
5
down vote

favorite











This article from The Guardian discusses Isaac Newton's investigation of the 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 seemsextremely aesthetic to me , 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?






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.











This article from The Guardian discusses Isaac Newton's investigation of the 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 seemsextremely aesthetic to me , 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?






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








edited 1 hour ago









m_goldberg

82.6k870190




82.6k870190






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asked 10 hours ago









Darko G

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Darko G is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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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
    10 hours ago











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











  • I'm sorry, I do not know how I managed to make such a ridiculous mistake.
    – Darko G
    9 hours 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
10 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
10 hours ago













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




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










1 Answer
1






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7
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
    9 hours ago










  • @BobHanlon, Modified, Thank you
    – Sachin Kumar
    8 hours ago










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1 Answer
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active

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1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

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up vote
7
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
    9 hours ago










  • @BobHanlon, Modified, Thank you
    – Sachin Kumar
    8 hours ago














up vote
7
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
    9 hours ago










  • @BobHanlon, Modified, Thank you
    – Sachin Kumar
    8 hours ago












up vote
7
down vote










up vote
7
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 8 hours ago

























answered 10 hours ago









Sachin Kumar

1727




1727







  • 1




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










  • @BobHanlon, Modified, Thank you
    – Sachin Kumar
    8 hours 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
    9 hours ago










  • @BobHanlon, Modified, Thank you
    – Sachin Kumar
    8 hours 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
9 hours ago




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












@BobHanlon, Modified, Thank you
– Sachin Kumar
8 hours ago




@BobHanlon, Modified, Thank you
– Sachin Kumar
8 hours ago










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









 

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