The Aurullia series are Tom Beddard‘s interpretation of a fractal formula called Mandalay, a specific type of Mandelbox with additional parameters that allow scaling of the folding on individual axes, either in parallel or one after.
Tom explains that the upside of Mandalay is that you can get an interesting mix of structures without the obvious patterns you often see in fractals. The curved domes are due to the Mandelbox like sphere folding and the towers due to the different fold scaling of individual axes.
He is also adding additional rotational changes between the images which helps create the transition from a crude unrefined state to a very geometric and architectural form, like different stages of a civilisation in the imaginary Kingdom of Aurullia – Tom.
Mandalay was first described (like all 3d fractal algorithms) on fractalforums.com.
Aurullia was created with Fractal-lab – a tool Tom Beddard has been building for the last few years that allows rendering of fractals in the browser with WebGL. More information about Fractal-lab can be found here.