"Mysteriously beautiful fractals are shaking up the world of mathematics and deepening our understanding of nature.
A fractal is "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity.
Fractals: they're famously found in nature and artists have created some incredible renderings as well. Fractals are purely a wonder -- too irregular for Euclidean geometry; iterative and recursive and seemingly infinite. They turn up in food and germs, plants and animals, mountains and water and sky."
I discovered computer fractal design in 1996, some 18 years ago, and have been joyfully playing with the creation of fractal design since that time. The first software program which I used was the venerable Ultrafractal and have used other programs since that time including Mandelbulb3d.
Fractals - Hunting the Hidden Dimension [PBS Nova]
The 'Octopostes marinis' lived in vast colonies in swampy areas during the Carboniferous period [359 million years ago].
Little is known about 'Octopostes marinis' other than that fact that had a rather curious habit of growth, in vast rows of five columns and that reproduction was by a form of mitosis. This can be seen in the second row of these fossil remains, where the parents have begun to split. The third row shows five young juveniles that have broken away from their parent cells and begun life on their own, and of course the parent is now a new cell itself.
The individual cell was eight sided, hence the Latin name Octopodes [from the Greek 'οκτώ όψης'] and though very small, they occurred in such incredibly large numbers the Octopodes are thought to be a major contributor to the vast coal deposits around the world.
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BTW, all of the above is pure fantasy. Time for me to reveal my 'Piltdown man' fossil fakery.
The 'Octopodes fossils' were found during a recent session with the Mandelbulb 3d software. Whereas most of the people who use Mandelbulb3d prefer to entertain situations and fantasies of future scenarios, I have found that this incedible fractal generation program is equally at ease in producing phenonmenal versions of the past, even if they are not necessarily true.
For a more detailed view of this 'fossil' image, visit my deviantArt page, and click on the enlargement button.
The Serenade No. 13 for strings in G major, K. 525 was written by Wolfgang Amadeus Mozart in 1787. The work is more commonly known by the title Eine kleine Nachtmusik. The German title means "a little serenade," though it is often rendered more literally but less accurately as "a little night music."
Somewhat surprised yesterday, while in the process of creating a new fractal image in Mandelbulb 3D, to suddenly be presented with Mozart's 'Eine kleine Nachtmusik'. There was no doubt in my mind, that this marvelous piece of music, which I had listened to countles times over the years, had mysteriously been transported into fractal form.
Have been working/playing with the Mandebulb 3D program for a couple of weeks now. And my enthusiasm for this fractal generation program knows no bounds. It is a wonderful combination of personal creativity and computer generated mystery. It is every child's world of fantasy and wonder as it becomes reality. Images which are soft and mysterious to shockingly crisp detail.
Also have a new site for displaying the most recent fractal designs in their larger sizes and vibrant detail.
Since encountering my first fractal image nearly 15 years ago I have been obsessed with this means of examing a previously unknown world. And have utilized a number of fractial software programs over the years. No more than a week ago I encountered a new program that renders fractal images in 3 D.
Mysteriously beautiful fractals are shaking up the world of mathematics and deepening our understanding of nature.
You may not know it, but fractals, like the air you breathe, are all around you. Their irregular, repeating shapes are found in cloud formations and tree limbs, in stalks of broccoli and craggy mountain ranges, even in the rhythm of the human heart. In this film, NOVA takes viewers on a fascinating quest with a group of maverick mathematicians determined to decipher the rules that govern fractal geometry.
For centuries, fractal-like irregular shapes were considered beyond the boundaries of mathematical understanding. Now, mathematicians have finally begun mapping this uncharted territory. Their remarkable findings are deepening our understanding of nature and stimulating a new wave of scientific, medical, and artistic innovation stretching from the ecology of the rain forest to fashion design. The Nova documentary highlights a host of filmmakers, fashion designers, physicians, and researchers who are using fractal geometry to innovate and inspire.
Discovered a new fractal program, Mandelbulb 3D, yesterday. Still learning the basics since the learning curve is pretty steep on most fractal programs.
It is available as a free download from: Fractal Forums, along with a 35 page read-me text which can serve as a basic tutorial. There are also several step-by-step tutorials on YouTube. And a very good web tutorial is available at Mandelbulb/Mandelbrot/fractals for beginners.
Almost immediately found one of the basic parameter images which appealed to me with little tweaking; a marvelous 'fractal box' which I saved and then added some text. It was a childhood fantasy which had suddenly become a reality, well in the virtual sense, a wonderfully detailed Treasure Chest. [Although most here know me as Jing-reed, my childhood name in Slovakia was Igor.]
As frequent visitors to this small niche of the internet know I have been intrigued by the Mandala art form for well over 25 years. Both the traditional Tibetan sand mandalas and thangkas as well as more contemporary forms, especially those produced by fractal design. I have been using the Ultrafractal software for well over ten years, one of the finest creative programs ever produced for the PC.
In common use, 'mandala' has become a generic term for any plan, chart or geometric pattern that represents the cosmos metaphysically or symbolically, a microcosm of the Universe from the human perspective. .
Two very important people in my life considered the Histories of Herodotus as an invaluable aid to the comprehension of life. The first was my father, a professor of history at Comenius University in Bratislava, Slovakia. The second was Gregorio Bartoni. himself Greek-Italian, and the love of my life. Unfortunately both of them succumbed to an early death, but both had left me with a legacy: that of the legendary Herodotus.
I have over the years had various copies of 'The Histories of Herodotus' in my possession, with passages underlined, and notes written in the margins, and then in my nomadic travels and changes of location, left them for someone else to enjoy and benefit from their wisdom. Recently felt the desire/need to once again have Heredotus by my side, and through the magic of the Internet downloaded yet another version for my Kindle Reader.
A new kind of literature, that of written history, was created by Herodotus. And it was through his efforts that many of the most famous accounts of antiquity have been preserved for us, such as the heroic stand of King Leonidas and the 300 Spartans at Thermopylae. It doesn't take much imagination to realize that 'The Lonely Planet', and all the other contemporary travel guides, had their beginning based on the fact that Herodotus was the first of the travel writers. His was an ability to collect and share accounts of his own travels, as well as the passing on of tales gathered from his fellow travelers. And yes, Count Almasy, also known as 'The English Patient', carried The Histories of Herodotus with him on all his travels.
Dr. Daniel Robinson, Philosophy Faculty, Oxford University / Professor Emeritus, Georgetown University in a lecture on Herodotus.
Herodotus and the Lamp of History - Part 1
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Herodotus and the Lamp of History - Part 2
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And I could not help but bring 'The Histories of Herodotus' into the 21st century with the creation of a fractal image which stylistically portrays but a representation of his many scrolls and and an inkpot used in the writing of his manuscrips all enveloped in the swirling mists of time.
The Apophysis image above was made by 'mynameishalo' , and is spectacular. And the YouTube videos by the same artist are wonderfully other worldly. Truly the stuff that dreams are made of - well, my dreams.
I have been using the Apophysis[and Ultra-fractal] software in order to make fractal images for years, and the images in the side panel [listed as 'Photo Albums' since I couldn't change the heading] are images from these two programs.
