# At The Helm Of The Burning Ship

Conference paper at EVA London 2019.

# 1 Citation

Claude Heiland-Allen. At the Helm of the Burning Ship. 2019. DOI: 10.14236/ewic/EVA2019.74

# 2 Abstract

The Burning Ship fractal is a non-analytic variation of the Mandelbrot set, formed by taking absolute values in the recurrence. Iterating its Jacobian can identify the period of attracting orbits; Newton’s root-finding method locates their mini-ships. Size estimates tell how deep to zoom to find the mini-ship or its embedded quasi-Julia set. Pre-periodic Misiurewicz points with repelling dynamics are located by Newton’s method. Stretched regions are automatically unskewed by the Jacobian, which is also good for colouring images using distance estimation. Perturbation techniques cheapen deep zooming. The mathematics can be generalised to other fractal formulas. Some artistic zooming techniques and domain colouring methods are also described.

# 2.1 Keywords

Burning Ship. Dynamical systems. Fractal art. Numerical algorithms. Perturbation theory.

# 3 Paper

The paper is available as open access from scienceopen.com.

A local mirror is here: AtTheHelmOfTheBurningShip-Paper.pdf.

# 4 Slides

The slides are here: AtTheHelmOfTheBurningShip-Slides.pdf.

# 5 Software

Related software is et (Linux) and Kalles Fraktaler 2 + (Windows, inc. WINE).

As of 2024, these are both abandonware, current development is in Fraktaler 3.

# 6 References

Many references in the paper PDF have link-rotted. Here they are with added archived versions: