Fractals in Weird Fiction by John Beal

“It is impossible to drop a pin without exciting a corresponding reaction in every Star. The action has disturbed the balance of the Universe.”
– Aleister Crowley, The Book of Thoth

The eloquence of Crowley’s understanding of what Chaos Physics now calls ‘The Butterfly Effect’ is evident in the above quote. He conceives a Universe where every point is interconnected, related in a grand ‘Strange Attractor/Repulsor’; where one event ultimately alters the destiny of events, millennia of light-years away.

His cosmic correspondences are echoed in the work of fiction The Plutonian Drug by Clark Ashton Smith. According to Dr Manners, the narrator of the story the drug creates… “unusual plastic images, not easy to render in terms of Euclidean planes and angles.” This incapability to be rendered in Euclidean Mathematics echoes fractals in that they are non-Euclidean, which means they do not comply with the generally accepted geometric shapes such as triangles, squares etc. The drug also creates another analogous property found in fractal images in that they both have artificial ‘cut-off points, or boundaries. The drug produced… “a vast distance that was wholly void of normal perspective, a weird and peculiar landscape stretched away, traversed by an unbroken frieze or bas-relief of human figures that ran like a straight undeviating wall.”

Apart from referring to the frieze as running like a straight wall, (a point which Smith expands upon to place branches along its surface) all the other descriptions can be regarded as being similar to that of many fractal images. Smith creates a vision of time as a strand of events – interjoined, constantly altering, all producing an abstract pattern. This strand is of ultimately infinite length and complexity, produced in a fractal dimension which cannot be accessed by Euclidean Mathematics, or by a normal state of mind. It is interesting to speculate whether the scientific concept of Time/Space could be modeled in fractal dimensional terms. Recent ideas of budding, bifurcating, universes, appear to suggest this as a possibility. John Dewey Jones, writing for the newsletter Amygdala expands upon the idea of fractals and the transcendence of the mind in his fiction concerning The Amygdalan Sects. (Note: Amygdala is derived from Almond shape, i. e. the shape of the Mandlebrot set, it is also the name of a section of the mid-brain which according to Mortimer Mishkin and Tim Appenzeller in their article for Scientific American of June 1987 is, along with the Hypothalamus, the processing plant and general linking area for sensory information, memory and desire.)

Jones writes of “The Brethren of the Hidden Path of Adepts”; monks who visualize the ‘object’ (Mandlebrot set) as a mandala, using it to transcend and enlighten themselves. He paints a landscape of decadence, where the old civilization has collapsed and the Brethren have to create the object as an astral image. To quote the Abbot of the Brethren: “We know that the eye can perceive details and gradations of color finer than any monitor can display. Just as the eyes are finer and more subtle than the monitor, so is the mind finer and more subtle than the eyes. And the soul is yet finer and subtler than the mind. Therefore, let the monk withdraw into a quiet place and withdrawing his senses like the limbs of a tortoise, let him fix his thoughts steadfastly upon the object.”

The Brethren recognise two paths to the object, The first through dreaming, obtaining visions of… “pure, jewel-like colors;.., patterns of abstract relationships: others said their dreams rhad] been too clear and distinct to describe in words.” This I feel relates to how H. P. Lovecraft produced some of his finest works of fiction, accessing knowledge through dreams, normally unobtainable.

However, Jones writes of the second method of path-working involving the object as the Abbot explains: “… rise at three in the morning and go to the summit of the mountain, sit.., and gaze steadfastly in the direction of Aldebaran – we don’t believe in any causal connection between Aldebaran and the object, you understand, but we have found the reddish light of that star to stimulate the mathematical vision we seek.” The Dreams in the Witch-House by Lovecraft seems to echo the first method of the Brethren in the dreams of the hero Walter Gilman. Lovecraft says of Gilman: “Possibly Gilman ought not to have studied so hard. Non-Euclidean calculus and quantum physics are enough to stretch the brain; and when one mixes them with folklore, and tries to trace a strange background of multi-dimensional reality behind the ghoulish hints of gothic tales and the wild whispers of the chimney-corner, one can hardly expect to be wholly free from mental tension.”

Gilman is lead by his interests into the domain of abstract mathematics… “beyond the utmost modern delvings of Plank, Heisenberg, Einstein and de Sitter.” Lovecraft describes Gilmans dream as… “plunges through limitless abysses of inexplicably colored twilight and baffling disordered sound; abysses whose material and gravitational properties… he could not even begin to explain.” He goes on… “The abysses were by no means vacant, being crowded with indescribably angled masses of alien-hued substance, some of which appeared to be organic while others seemed inorganic… Gilman sometimes compared the inorganic matter to prisms, labyrinths, clusters of cubes and planes… and the organic things struck him variously as groups of bubbles, octopi, centipedes, living Hindu idols, and intricate arabesques roused into a kind of ophidian animation.”

Fractal doubles of these images can be discovered in many of the books on the subject. Mandlebrot in The Fractal Geometry of Nature describes and shows pictures of Appolonian nets, Cantor and Fatou dust – near-fractals that display distinct bubbling, similar to clusters of cubes and planes: Koch/Peano snowflake curves that look intensely like mazes. Other geometrical designs which are featured are the Mandlebrot set, Julia set, squigs (as the name implies a squiggle design) all having similarities to octopi, centipedes and intricate arabesques. The design called ‘Hindu idols’ by Lovecraft can be imagined in two ways, either as the ‘body-shape’ of Michael Barnsley’s development on fractals in his book Fractals Everywhere, or as biomorphs, sigil-like designs fractally produced, which evolve like living organisms into multifarious forms.

At the end of the story Lovecraft describes Azathoth as the Ultimate Chaos – similar to a jewelled Mandlebrot set in an all-enveloping crown. Other stories by Lovecraft also allude to bizarre images of Fractal Geometry. Examples are: At the Mountains of Madness Where he uses abstract geometry to describe the ancient city of the Old Ones; and Through the Gates of the Silver Key, where the abstract patterns observed by Randolph Carter on the threshold of the gate are reminiscent of the flowing, bifurcating forms of fractals. Lovecraft’s use of fractal images in Through the Gates of the Silver Key, is reminiscent of Smith’s in The Plutonian Drug, since both are describing voyages through Space/Time. As example of this Randolf Carter, the hero of Lovecraft’s story, upon using the silver key is surrounded by… “dim half-pictures with uncertain outlines amidst the seething Chaos, but Carter knew they were of memory and imagination only. Yet he felt that it was not chance which built these things in his consciousness, but rather some vast reality, ineffable and undimensional, which surrounded him and strove to translate itself into the only symbols he was capable of grasping.”

Algernon Blackwood’s The Pikestaffe Case uses abstract geometry’s to enable ‘Pikestaffe’ to perform an ‘Alice through the looking -glass’ trip into an extra – dimension. Pikestaffe’s blackboard was covered in diagrams that “pe rhaps were Euclid, or possibly astronomical.” He also had notes which have fractal equivalents; for example Pikestaffe’s landlady discovered notes with a diagram that she described thus: “In the centre, surrounded by scriggly hieroglyphics, numbers, curves and lines meaningless to her, she saw a diagram of the full-length mirror.”

The last piece of fiction I would like to mention which is similar to the fractal geometry’s of Mandlebrot, Julia, Cantor and others is The Hounds of Tindalos by Frank Belknap Long. In his story, Long uses very similar concepts to those in Smith’s The Plutonian Drug and Lovecraft’s Through the Gates of the Silver Key, enabling the main character Halpin Chalmers to traverse back into time into the ultimate abyss of chaotic geometry.

Thus all these stories are like chambers in the “Witch-House” – the house on the borderland of an abyss where dwell incredible “Mathematical Monsters.”