Fractal Magic by Abysimus

  1. Imagine yourself seated in a room facing a window that occupies an entire wall. Imagine further that this window has the magical property that it opens on a scene identical with the landscape of your mind. Think of it as a device that transforms your imagination into a tangible visible reality. This is in no way analogous to a television screen. Rather, envision downtown Paris seen from the gondola of a hot air balloon. That is the difference. So, if the scene in your mind envisions surfing the quantum foam, that is also the scene outside the window. If the scene in your mind is the Unseen University Library (including orangatang librarian), that is the scene outside.

    A very important characteristic of this window is that if you choose to see (for example) the Unseen University Library (including orangatang librarian), that is what you really see, not some fictitious representation. For those of you wearing a quizzical expression, do a Google image search. This same "reality characteristic" is true for whatever you choose to see. Because in an infinite universe, (if this is an infinite universe) whatever you choose to see exists in reality somewhere. I have been toying with this idea for years and have made several still renderings of magic windows. For example, a rendering of this name (i.e. Finestra Magica) is on display in one of my galleries. Doubtless, I will make several more. It all depends on what is on (or in) my mind.

    I decided to make a video on this theme because I did not feel that any of the still images I historically have created elaborated sufficiently the potential scope available from such a magical device. Naturally, no two viewers looking out of the window will see the same scene. Nor do I expect that anyone who views this video would imagine what I have depicted here. What I have depicted here are scenes from a personal voyage. What I hope viewers will be thinking is "Wow! If I had such a magical window what would I choose to see?" And the answer to that question (which only you know) will be quite illuminating on a personal level.

    In the final analysis, of course, my principal objective in this (as in all of my videos) has been to create something both magical and beautiful.

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  2. I remain perpetually enthralled by multidimensional realities. Quaternion fractal dimensions afford an infinite playground, which enables the visualization of beautiful landscapes and fanciful denizens of unseen worlds.

    The term ‘Quaternion’ is used in both theoretical and applied mathematics. In the context of fractal geometry, quaternions define a four dimensional space. Since we humans live in only three spatial dimensions (up-down, right-left, forward-backward), we are not physically equipped to experience a fourth spatial dimension.

    Nevertheless, the fourth spatial dimension exists. In fact, wide varieties of spatial dimensions and one time dimension exist (as demonstrated in quantum mechanics). What fractal quaternions allow us to do is ‘rotate’ the fourth dimensional plane of a structure into three-dimensional space so that we can visualize it. For example, we think of a sphere as a ‘ball’ (which, in three-dimensional space it is). But in four-dimensional space, a sphere assumes many exotic and beautiful shapes (depending on the fractal involved).

    Of course, the fourth dimensional image we ‘see’ using this technique is not what it ‘really’ looks like. What we see is only the shadow of the fourth-dimensional plane. If we could ‘actually’ see it, I am not altogether convinced we would emerge from the experience with our sanity intact. You, dear reader, for example, would in no way recognize yourself in the fourth dimension. Still, since my sanity is only tenuous anyway, I do not find the prospect daunting.

    Every image in this video is some species of four-dimensional quaternion. I will not cite them all here because they would only be meaningful to geeks like me anyway (and you know who you are). Besides, I might be accused of pomposity and that is not a sobriquet that befits me. The music, as is my recent wont, is morphed by me using sound processing of various pieces obtained from the public domain to form a collage. Since the result is a unique composition, no attribution is made.

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  3. Fractal imagery is all about the use of light (hence the title of this video). There are hundreds of mathematical algorithms dedicated to various techniques applicable to light and color expression. Likewise, there are hundreds of mathematical formulas designed specifically to express geometries of individual fractal structures. Some of these structures (such as the well-known Mandelbrot set) are familiar to many. New structures are being discovered regularly and I suspect that the variety yet to be found is infinite. Fractal artists speak incessantly of finding the fractal 'holy grail'. Such a formula will probably prove to be as elusive as the original article.

    I have been working with fractals both professionally and artistically for more than thirty years. At the present time, I no longer draw a distinction between the two. The professional work has all been dedicated to scientific explorations into fractal structures in natural ecosystems. The artistic work tends to express the scientific work (not just mine, but that of others as well) in the context of demonstrating the ubiquitous fractal structures that comprise the entire universe in which we live. Galaxies are fractal structures. Atoms are fractal structures. And so is everything in-between.

    When you see something in my work that looks like a tree, or looks like a flower, or anything else; the resemblance is not accidental. The entire universe is fractal and the central impetus behind all of my work lies in trying to capture and illustrate the inseparable relationship between this and the divine genius underlying it all. It is my conviction that artistic expression of this inseparable relationship must produce something that is beautiful. That is, it must do so if my competence is equal to the task. My own personal view is that my competence is equal to the task but just barely. If perfect expression is one mile high, I am less than an inch tall.

    As it happens, however, I find the process meditatively rewarding. It is sort of like being the garden itself rather than just looking at one. Besides, being less than an inch tall gives me all of the advantages Alice had and I plan to enjoy the ride.

    I hope you like my latest offering.

    The music here is morphed by me using sound processing software to alter and merge various pieces obtained from the public domain to form a collage. Since the result is a unique ten-minute composition made specifically for this video, no attribution is made.

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Fractal Magic by Abysimus


The stunning genius of creation. From the infinitely large to the infinitely small and throughout countless measures in between, the universe is fractal. Once this was a speculative hypothesis; it is now established fact. Fractal manifestations are…

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The stunning genius of creation. From the infinitely large to the infinitely small and throughout countless measures in between, the universe is fractal. Once this was a speculative hypothesis; it is now established fact. Fractal manifestations are everywhere. A hundred billion swirling stars spill across the velvet blackness of space, branches of lightning split the darkness, crashing thunder rocks the earth, the iridescent eyes of a dragonfly shine in a momentary pause of frenetic flight, the quantum entanglement of life weaves a vast tapestry of infinite complexity. Once you learn to look for the telltale recursive signposts, you will see fractals everywhere you look.

A truth that is both so fundamental and so universal should be the source of immense scientific and philosophical interest. And, as a matter of fact, it has been. Unfortunately, however, the sheer immensity of the revelation serves to obscure its import. The subject of fractals has been developed to a wondrous level of mathematical intricacy. Scholarly tomes on the subject abound. Although it is conceptually elegant and quite simple (as are all great theorems), its permutations are quite literally infinite. This fact raises interesting considerations for we humans and the nature of the reality we inhabit. I have explored these considerations elsewhere.

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