Painting with Diophantine Equations
Solutions of the Diophantine equations xl + ym = zn have been used for the generation of these pictures. The solutions in the x-y plane can be found as black dots in the pictures. Functions fi(x,y) are assigned to each dot i and combined together. They are forming mountains, to which colorful contour lines have been assigned.
Formule
- x^2 + y = z^2
Diophantos No 1
-100 < x < 100
-100 < y < 100
Trivial solutions with x=0 or y=0 have been excluded.
Formule
- x^2 + y^2 = z^2
Diophantos No 2
Pythagorean triples
-100 < x < 100
-100 < y < 100
Trivial solutions with x=0 or y=0 have been excluded.
Formule
- x^2 + y^2 = z^2
Diophantos No 3
Pythagorean triples
-100 < x < 100
-100 < y < 100
Trivial solutions with x=0 or y=0 have been excluded.
Formule
- x^2 + y^2 = z^3
Diophantos No 4
-100 < x < 100
-100 < y < 100
Trivial solutions with x=0 or y=0 have been excluded.
Formule
- x^2 + y^2 = z^4
Diophantos No 5
-50 < x < 50
-50 < y < 50
Trivial solutions with x=0 or y=0 have been excluded.
Formule
- x^2 + y^2 = z^4
Diophantos No 6
-100 < x < 100
-100 < y < 100
Trivial solutions with x=0 or y=0 have been excluded.
Formule
- x^2 + y^2 = z^4
Diophantos No 7
-100 < x < 100
-100 < y < 100
Trivial solutions with x=0 or y=0 have been excluded.
Formule
- x^2 + y^2 = z^4
Diophantos No 8
-150 < x < 150
-150 < y < 150
Trivial solutions with x=0 or y=0 have been excluded.
Formule
- x^2 + y^2 = z^4
Diophantos No 9
-200 < x < 200
-200 < y < 200
Trivial solutions with x=0 or y=0 have been excluded.
Formule
- x^2 + y^2 = z^4
Diophantos No 10
-200 < x < 200
-200 < y < 200
Trivial solutions with x=0 or y=0 have been excluded.
Formule
- x^2 + y^2 = z^4
Diophantos No 11
-200 < x < 200
-200 < y < 200
Trivial solutions with x=0 or y=0 have been excluded.
Formule
- x^2 + y^3 = z^2
Diophantos No 12
-100 < x < 100
-100 < y < 100
Trivial solutions with x=0 or y=0 have been excluded.
Formule
- x^3 + y = z^2
Formule
- x^3 + y^3 = z^2
Formule
- x^3 + y^3 = z^2
Formule
- x^4 + y^2 = z^2
Diophantos No 16
-100 < x < 100
-100 < y < 100
Trivial solutions with x=0 or y=0 have been excluded.
Formule
- x^4 + y^2 = z^2
Diophantos No 17
-100 < x < 100
-100 < y < 100
Trivial solutions with x=0 or y=0 have been excluded.
Formule
- x^4 + y^3 = z^2
Diophantos No 18
-100 < x < 100
-100 < y < 100
Trivial solutions with x=0 or y=0 have been excluded.
Formule
- x^4 + y^4 = z^3
Diophantos No 19
-500 < x < 500
-500 < y < 500
Trivial solutions with x=0 or y=0 have been excluded.
Formule
- x^4 + y^4 = z^3
Diophantos No 20
-500 < x < 500
-500 < y < 500
Trivial solutions with x=0 or y=0 have been excluded.
Formule
- x^6 + y^4 = z^2
Diophantos No 21
-100 < x < 100
-100 < y < 100
Trivial solutions with x=0 or y=0 have been excluded.
Formule
- x^6 + y^4 = z^2
Diophantos No 22
-100 < x < 100
-100 < y < 100
Trivial solutions with x=0 or y=0 have been excluded.
