# Fractals

## Fractal Gallery

Welcome to Geoff Swift's fractal gallery. For best results, watch the videos full screen on the YouTube website. For technical details on of these videos, please also refer to the Wikipedia links and the text on YouTube which accompanies each video. Other videos may be found on Geoff's YouTube channel.

### Multibrot Sets

These fractal videos are morphs between multibrot sets generated with varying exponent values. De Moivre's formula is used to generalise common fractal formulas, such as the Mandelbrot Set, Mandelbar / Tricorn and the Burning Ship.

#### Distance Estimation (DEM/M)

These two videos are created using the Distance Estimatation Method for Mandelbrot sets (DEM/M).

The first video uses the classic Mandelbrot formula, and includes the quadratic, cubic and quartic Mandelbrot sets.

The second video is the same but rendered with an inverted plane, so the shapes are similar but are shown inside out. When the Mandelbrot Set appears in the video, it is shaped like a teardrop.

#### Escape Time Algorithm (ETA/M)

These three videos are created using the Escape Time Elgorithm for Mandelbrot sets (ETA/M).

The first video uses the classic Mandelbrot formula, and includes the quadratic, cubic and quartic Mandelbrot sets.

The second video also varies the value of the exponent, but uses the complex conjugate in the calculation and so produces a Mandelbar/Tricorn shape.

The third of these Multibrot videos is similar, but uses the Burning Ship fractal formula instead.

### Inverted Multibrots

The same Multibrot formulae can be rendered with the complex plane inverted. This entails an initial step of calculating the multiplicative inverse of each point in the complex plane.

Here's an inverted Mandelbrot power morph.

Here's an inverted Mandelbar power morph.

Here's an inverted Burning Ship power morph.

### Julia Sets

The following YouTube videos are Julia set morphs with colour cycling.

To produce these videos, custom software was developed by Geoff Swift using C++ and Cinder.