Mixing
Newton's cubic curve
Clash Royale CLAN TAG#URR8PPP
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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
asked 2 hours ago
Darko G
111
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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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add a comment |Â
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
asked 2 hours ago
Darko G
111
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 isx^3 - b x - 4 y^2 + 1 == 0. You are missing a constant, and theb xterm 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 ofxto 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
add a comment |Â
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
asked 2 hours ago
Darko G
111
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
asked 2 hours ago
Darko G
111
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.
asked 2 hours ago
Darko G
111
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.
asked 2 hours ago
Darko G
111
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.
asked 2 hours ago
Darko G
111
asked 2 hours ago
Darko G
111
111
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.
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.
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 isx^3 - b x - 4 y^2 + 1 == 0. You are missing a constant, and theb xterm 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 ofxto 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
add a comment |Â
2
Well, you seem to have done your substitutions incorrectly. The correct equation you should plot isx^3 - b x - 4 y^2 + 1 == 0. You are missing a constant, and theb xterm 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 ofxto 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
add a comment |Â
1 Answer
1
active
oldest
votes
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: 
answered 2 hours ago
Sachin Kumar
1427
1
You can maintain sharpness while increasing the number of steps (b, -8, 8, 1/2) by usingContourStyle -> Directive[Thin, Black]
– Bob Hanlon
1 hour ago
@BobHanlon, Modified, Thank you
– Sachin Kumar
5 mins ago
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
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:
answered 2 hours ago
Sachin Kumar
1427
1
You can maintain sharpness while increasing the number of steps (b, -8, 8, 1/2) by usingContourStyle -> Directive[Thin, Black]
– Bob Hanlon
1 hour ago
@BobHanlon, Modified, Thank you
– Sachin Kumar
5 mins ago
add a comment |Â
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:
answered 2 hours ago
Sachin Kumar
1427
1
You can maintain sharpness while increasing the number of steps (b, -8, 8, 1/2) by usingContourStyle -> Directive[Thin, Black]
– Bob Hanlon
1 hour ago
@BobHanlon, Modified, Thank you
– Sachin Kumar
5 mins ago
add a comment |Â
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:
answered 2 hours ago
Sachin Kumar
1427
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:
answered 2 hours ago
Sachin Kumar
1427
edited 7 mins ago
answered 2 hours ago
Sachin Kumar
1427
answered 2 hours ago
Sachin Kumar
1427
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 usingContourStyle -> Directive[Thin, Black]
– Bob Hanlon
1 hour ago
@BobHanlon, Modified, Thank you
– Sachin Kumar
5 mins ago
add a comment |Â
1
You can maintain sharpness while increasing the number of steps (b, -8, 8, 1/2) by usingContourStyle -> 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
add a comment |Â
Darko G is a new contributor. Be nice, and check out our Code of Conduct.
Darko G is a new contributor. Be nice, and check out our Code of Conduct.
Darko G is a new contributor. Be nice, and check out our Code of Conduct.
Darko G is a new contributor. Be nice, and check out our Code of Conduct.
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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 theb xterm 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 ofxto 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