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matematik & programmering

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## Make Fractals of Images

Select an image and then generate a Julia set or a Mandelbrot set.

## Orbit Trap Fractals

Generate Julia sets and the Mandelbrot set using four different, and adjustable, orbit traps.

## Animate Julia Sets

Interactive Julia set, animation bewteen two Julia sets, and basic information about Julia sets.

## Möbius Transformation of a Doyle Spiral

Interactive Möbius transformation of a Doyle Spiral.

## Rolling Hypocycloids and Epicycloids

Interactive examples of rolling hypocycloids, epicycloids and similar shapes.

## Focal Points, Ellipses and Ovals

Interactive three-pins-and-a-string-blob, three-ellipse, and three foci variant of Cassini oval.

## Make Hyperbolic Tilings of Images

Select an image, or take a photo if using mobile device. Move the image if needed. Choose p and q. Generate a tiling.

## Interactive Hyperbolic Tiling in the Poincaré Disc

A draggable interactive hyperbolic tiling using the Poincare disc model.

## The Mandelbrot Set

Make successive zooms of the Mandelbrot set. The area picked is displayed in one canvas, the result is shown in another canvas.

## Interactive Lorenz Attractor

Interactive Lorenz attractor with 10,000 blue butterflies under the Lorenz attractor flow.

## Variations on Pythagoras' Tree ♦

By using the points defining the squares of an animated Pythagoras' tree, it is possible to draw various paths to create a variety of animations.

## Inversion in Circle ♦

A review of those properties of circle inversion that are needed in order to construct hyperbolic tools.

Raplaced the non-functional old GeoGebra applet with a Processing-version of the interactive Apollonian gasket.

## Non-Euclidean Geometry ♦

I made a new section about non-Euclidean geometry. For now it's just an introduction.

## Paint Circle-Inverted Mondrian! ♦

Make a painting in Mondrian style. The painting is inverted in a circle as you paint.

## How to Make a Cubic Bézier Spline ♦

Splines are used to draw smooth curves. The construction of a cubic Bézier spline is explained and visualized.

## De Casteljau's Algorithm ♦

De Casteljau's algrithm is used to draw Beziér curves. Bézier curves are used when making smooth curves defined by points along a path.

## Damped Lissajous Curves ♦

If two perpendicular pendulums are used to control the movement of a pen, the curve traced out is a so called damped Lissajous curve.

## Newton Fractals ♦

Imagine three coloured regions bordering to each other such that all three regions have exactly the same border!

## Modelling 3D illusions ♦

The human brain uses shadows to interpret how objects move. By faking the shadow, one can fake the perceived motion of an object.