Constant Value

When everytime you ask "why?", you get the same answer.

0 = y + -1

β + -1

JSON: { "0,1": "1", "0,0": "-1" }

calc: y + -1

GLSL: y+-1.0

Line

The most linear polynomials are known as lines.

0 = x + -1y

α + -1β

JSON: { "1,0": "1", "0,1": "-1" }

calc: x + -1*y

GLSL: x+-1.0*y

Parabola

An expression in parables.

0 = x² + -1y

α² + -1β

JSON: { "2,0": "1", "0,1": "-1" }

calc: x^2 + -1*y

GLSL: x*x+-1.0*y

Inverse Parabola

An unexpression in parables.

0 = x^-2 + -1y

-1β / α²

JSON: { "-2,0": "1", "0,1": "-1" }

calc: x^-2 + -1*y

GLSL: 1.0/(1.0*x*x*1.0)+-1.0*y

Hyperbola

A hyperbolic experience.

0 = -1 + xy

-1 + αβ

JSON: { "0,0": "-1", "1,1": "1" }

calc: -1 + x*y

GLSL: -1.0+x*y

Circle

A circle.

0 = -1 + x² + y²

-1 + α² + β²

JSON: { "0,0": "-1", "2,0": "1", "0,2": "1" }

calc: -1 + x^2 + y^2

GLSL: -1.0+x*x+y*y

Fermat Curve

A Fermat curve.

0 = -1 + x³ + y³

-1 + α³ + β³

JSON: { "0,0": "-1", "3,0": "1", "0,3": "1" }

calc: -1 + x^3 + y^3

GLSL: -1.0+x*x*x+y*y*y

Folium of Descartes

A folium of Descartes.

0 = x³ + -3xy + y³

α³ + -3αβ + β³

JSON: { "3,0": "1", "1,1": "-3", "0,3": "1" }

calc: x^3 + -3*x*y + y^3

GLSL: x*x*x+-3.0*x*y+y*y*y

Lemniscate of Bernoulli

A lemniscate of Bernoulli.

0 = -2x² + x⁴ + 2y² + 2x²y² + y⁴

-2α² + α⁴ + 2β² + 2α²β² + β⁴

JSON: { "2,0": "-2", "4,0": "1", "0,2": "2", "2,2": "2", "0,4": "1" }

calc: -2*x^2 + x^4 + 2*y^2 + 2*x^2*y^2 + y^4

GLSL: -2.0*x*x+x*x*x*x+2.0*y*y+2.0*x*x*y*y+y*y*y*y

Lemniscate of Gerono

A lemniscate of Gerono.

0 = -1x² + x⁴ + y²

-1α² + α⁴ + β²

JSON: { "2,0": "-1", "4,0": "1", "0,2": "1" }

calc: -1*x^2 + x^4 + y^2

GLSL: -1.0*x*x+x*x*x*x+y*y

quartic⁴

A quartic polynomial.

0 = 8 + -5x + 4x³ + -1x⁴ + -1y

8 + -5α + 4α³ + -1α⁴ + -1β

JSON: { "0,0": "8", "1,0": "-5", "3,0": "4", "4,0": "-1", "0,1": "-1" }

calc: 8 + -5*x + 4*x^3 + -1*x^4 + -1*y

GLSL: 8.0+-5.0*x+4.0*x*x*x+-1.0*x*x*x*x+-1.0*y

Jumping Jack

0 = -1 + 48xy + -64x²y + -64xy²

-1 + 48αβ + -64α²β + -64αβ²

JSON: { "0,0": "-1", "1,1": "48", "2,1": "-64", "1,2": "-64" }

calc: -1 + 48*x*y + -64*x^2*y + -64*x*y^2

GLSL: -1.0+48.0*x*y+-64.0*x*x*y+-64.0*x*y*y

Phi (φ)

0 = -1x² + -1xy + -1y²

-1α² + -1αβ + -1β²

JSON: { "2,0": "-1", "1,1": "-1", "0,2": "-1" }

calc: -1*x^2 + -1*x*y + -1*y^2

GLSL: -1.0*x*x+-1.0*x*y+-1.0*y*y

Hippopede

0 = -4x + x⁴ + -1y² + 2x²y² + y⁴

-4α + α⁴ + -1β² + 2α²β² + β⁴

JSON: { "1,0": "-4", "4,0": "1", "0,2": "-1", "2,2": "2", "0,4": "1" }

calc: -4*x + x^4 + -1*y^2 + 2*x^2*y^2 + y^4

GLSL: -4.0*x+x*x*x*x+-1.0*y*y+2.0*x*x*y*y+y*y*y*y