Under the water under the sea how many Nautilus can you see?

 

'Captain Nemo dives again' -digital art George Roberts March 2024.

The Nautilus both extant and extinct, are characterized by involute or more or less convolute shells that are generally smooth, with compressed or depressed whorl sections, straight to sinuous sutures, and a tubular, generally central siphuncle. Having survived relatively unchanged for hundreds of millions of years, nautiluses represent the only living members of the subclass Nautiloidea, and are often considered "living fossils" -Wikipedia

The shells follow the mathematics of a logarithmic curve. All but one of the above were generated as fractals created in the software INCENDIA. 

Spring

 

'Spring' digital art by George Roberts
 March 2024 INCENDIA software.

I have become digitally obsessed by the magic of fractals and recursive algorithms. They are literally a force of nature. I will need to join a support group - 'Fractals Anonymous'

"Thorns and briars grow around the Castle, and soon it is almost invisible and nearly forgotten. A passing Prince, and his father the King hear of the legend of “The Sleeping Beauty”, and Prince Florimond declares he will rescue her from her sleep"

Ferntastic fractals

 

'Seeds and ferns' - digital painting by George Roberts
 using INCENDIA fractal software and Affinity Photo2

The infinitely recursive universe of fractals, provides a multiplicity of brushes, colours, textures and lighting for the digital artist to explore. This is such a surprising journey full of wonderful artistic and unconsidered events at all possible scales.

The ancient dragon swallows it’s scary, scaly tail

between

two mirrors parallel and recursive bound.

The artist daubs a painterly fairy tale,

between

 two dimensions and with marks on gesso ground.

All protagonists and time

await an unexpected and infrequent visitation,

 which in itself will announce an act of creation.

George Roberts

 

The fractal universe in a nutshell.

 

'Fractal blossom' - digital painting George Roberts March 2024

'Tardigrade' digital painting - George Roberts March 2024

'It's life Jim but not as we know it' - digital painting George Roberts March 2024

These images were constructed and rendered using the mathematics of fractals and the excellent and powerful freeware INCENDIA and Mandelbulb 3d. Many thanks to Prof GP for recommending this software. The above images were finally composed using Affinity Photo 2 software.

All fractals show some self-similarity. If you look ever closer into the details of a fractal, you observe multiple replicas of the whole.

Fractals can often be seen in nature. A fern is a classic example, with each of the branches coming off the main stem being similar to the entire frond. They are self-similar to the original but on a smaller scale.

These self-similar patterns are the result of a simple equation or mathematical statement. You create  a fractal algorithm by repeating this equation through a feedback loop. This process is called iteration  with the results of one iteration forming the input value for the next.

The patterns created by these algorithms often have fractal dimensions that are not whole numbers. Fractal dimension is a measure of shape complexity. Fractals are also recursive irrespective of scale - repeating themselves endlessly.

What is important is to spread confusion, not eliminate it.

 

'Salvador Dali in the 3rd Person'
digital painting by George Roberts March 2024
The image was created using
Mandelbulb 3d and Affinity Photo 2 software. 

In memory of my university flat mate Paul, who had tea with Dali in his surreal garden with the giraffe in Spain many moons ago.

The longer I live the more surreal the world in which I live becomes - here's to you Paul and Salvador!

“Those who do not want to imitate anything, produce nothing.”

― Salvador Dalí

.

A Goat by moonlight in a fractal landscape

 

'A goat by moonlight in a fractal landscape' by George Roberts digital art . Credit:: Mandelbulb 3d software

Thanks to the excellent Greg P for bringing 'Mandelbulbs' to my attention. Credit to the brilliant freeware Mandelbulb.3D, which was used to create this fractal landscape. Mathematics is the digital artist's infinitely flexible brush and medium. 

"On a bluff, on a bluff, on a bluff stood billy-goat Gruff"