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.