Function graphers, visualisation

Table of contents

1. Real functions
2. Implicit functions
3. Parametric equations
4. Discrete functions
5. Inequalities
6. Initial value problems
7. Bivariate functions
8. Parametric surfaces
9. Implicit surfaces
10. Vector fields
11. Complex functions
12. Complex dynamics

Real functions

• A function.
• Several functions.
• A function and its derivative.
• A function and its first three derivatives.
• Zeros of a function.
• A tangent of a function.
• An antiderivative.
• Integral representation of the gamma function.
• A family of functions.
• A distinction of cases.
• An interpolation polynomial.
• A family of interpolation polynomials.
• Table for a function.
• Slider for one parameter.
• Sliders for two parameters.
• Partial sum of a Fourier series.

Implicit functions

• An implicit function.
• An implicit function and its asymptotes.
• A family of implicit functions.
• Lemniscate of Gerono.

Parametric equations

• The unit circle.
• The lemniscate of Gerono.
• A spiral.
• An Euler spiral.
• A helix.
• A family of parametric curves.
• Metamorphosis.
• Applying a rotation matrix.
• Applying a family of rotation matrices.
• Tangential vector of a curve.
• TN-frame.
• Osculating circle.
• A smooth star.

Discrete functions

• A sequence, explicitly defined.
• A sequence, recursively defined.
• A sequence and some bounds.
• A series.
• Euler's totient function.
• A random walk.
• Hofstadter's Q sequence.
• Table for a sequence.
• Value list for a sequence.

Inequalities

• An inequality in one variable.
• An inequality in two variables.
• A system of inequalities. Covering visible.
• Solution set of that system.

Initial value problems

• A first order ODE. Initial state is given by p:=[x0,y(x0)].
• A second order ODE. Initial state is given by p:=[x0,y(x0),y'(x0)].
• For a function of time.
• Slope field of a first order ODE.
• A Picard iteration.
• Solving a system by matrix exponential.
• An autonomous system of two ODE.
• A non-autonomous system of two ODE.
• Phase portrait of the damped pendulum. Stream lines.
• The one body problem. Stroboskopic view.
• The one body problem as a first order system.
• Scattering at a Coulomb potential.
• The Lorenz attractor. Projection on the xz plane.

Bivariate functions

• A bivariate function. Transparent graph.
• A bivariate function in perspective projection.
• Heatmap. Transparent graph.
• Displacement of the coordinate system.
• Smaller tile resolution. Takes some computing time.
• Lifting a curve on a surface.
• A bivariate function with a level curve.
• A bivariate function with many level curves.
• Level curves in the xy-plane. With periodic heat map.
• Slider for one parameter.
• Sliders for two parameters.

Parametric surfaces

• The unit ball.
• A torus.
• Dini's surface.
• A curve on a torus.

Implicit surfaces

• The unit ball.
• A hyperboloid.
• A torus.
• Slider for one parameter.
• Sliders for two parameters.

Vector fields

• A vector field. Stream lines.
• Slope field of an ODE. Stream lines.
• A slope field and solution curves.
• Gradient field of a scalar field.
• A linear coordinate mapping. As a matrix.
• A non-linear coordinate mapping.
• A rotation matrix.

Complex functions

• The Gamma function.
• A complex function at given scale.
• Relief of a complex function.
• Apply a complex mapping to the coordinate grid.
• A complex valued function.
• A complex valued function as a parametric curve.
• Real part, imaginary part und absolute value of a complex values function.
• Derivative of a complex function.
• Integral representation of the complex logarithm.
• Integral representation of the gamma function.
• A Riemann surface.

Complex dynamics

• The Mandelbrot set. Color shift.
• The Mandelbrot set at given position and scale.
• The Mandelbrot set with N iterations and n*n samples.
• A Julia set.
• A Julia set at given position and scale.
• A Newton fractal.
• Newton fractal from initial value zero for a family of cubic polynomials.
• Bifurcation diagram of the logistic map.