FormulaToy.net Examples:

Cartesian Coordinates: f(x,y,z)

• 
  z = x^2 - y^2
• 
  z =
  -1/(x^2 + y^2)
• 
  z =
  sin(pπ(x^2+y^2))/
  (pπ(x^2+y^2))

  Use the slider to change 'p'.

• 
  z = x^2 + y^2

Cylindrical Coordinates: f(radius,Φ,z)

• 
  r = 1
• 
  r = cos(z*4)
• 
  z = cos(Φ*4)*r
• 
  r = sin(zπ)

Spherical Coordinates: f(radius, Φ, θ)

• 
  r = sin(3θ)
• 
  θ = exp(|cos(4Φ)|/π) + r/2
• 
  r = sin(θ)*cos(2Φ)
• 
  r = θΦ
• 
  r = sin(3θ)*sin(2θ)

Parametric equations: f(x,y,z)

• 
  Figure 8 torus: Klein bottle immersion
• 
  Catenoid
• 
  Mobius Strip
• 
  Umbilic Bracelet
• 
  Enneper Surface
• 
  Figure 8 Knot

Torus Knots

• 
  A (3,1) knot

  A trefoil

• 
  A (3,7) knot
• 
  A (3,11) knot
• 
  A (4,23) knot
• 
  A polynomial parameterization of a trefoil knot. More here.

Complex Functions and (Simple) Riemann Surfaces

• 
  f=sqrt(g)
• 
  f=log(g)
• 
  Lambert W Function
• 
  f=atan(g)
• 
  g=1/(1+f^2)