Plot the Kampyle of Eudoxus with gnuplot

Question

I wish to generate the Kampyle of Eudoxus with Gnuplot:

plot x*x*x*x = x*x + y*y

This code should do the trick. However, it returns me the following error:

plot x*x*x*x=x*x+y*y
            ^
"file.plt", line 1: unexpected or unrecognized token

Is there a way to plot this?

Answer 1

If you check the gnuplot FAQs you will find a note that you cannot plot implicit defined graphs directly, however, a workaround is described.

Default samples is 100. So, in order to increase precision set samples 1000 and set isosamples 1000.

Script:

### plot implicit graph
reset session

f(x,y) = x**4 - a*(x**2 + y**2)
a = 1

set samples    1000
set isosamples 1000
set contour base
set cntrparam levels discrete 0.0
unset surface
set table $CONTOUR
    splot f(x,y)
unset table
set key top center

plot $CONTOUR w l lc "red" ti sprintf("\n\nKampyle of Eudoxus\nx^4 = a*(x^2 + y^2)\na = %g",a)
### end of script

Result: