FractAlphic Frolix

A fractal is a shape that contains smaller (and smaller) versions of itself, like this:

The hourglass fractal


Fractals also occur in nature. For example, part of a tree looks like the tree as whole. Part of a cloud or a lung looks like the cloud or lung as a whole. So trees, clouds and lungs are fractals. The letters of an alphabet don’t usually look like that, but I decided to create a fractal alphabet — or fractalphabet — that does.

The fractalphabet starts with this minimal standard Roman alphabet in upper case, where each letter is created by filling selected squares in a 3×3 grid:


The above is stage 1 of the fractalphabet, when it isn’t actually a fractal alphabet at all. But if each filled square of the letter “A”, say, is replaced by the letter itself, the “A” turns into a fractal, like this:








Fractal A (animated)


Here’s the whole alphabet being turned into fractals:

Full fractalphabet (black-and-white)


Full fractalphabet (color)


Full fractalphabet (b&w animated)


Full fractalphabet (color animated)


Now take a full word like “THE”:



You can turn each letter into a fractal using smaller copies of itself:







Fractal THE (b&w animated)


Fractal THE (color animated)


But you can also create a fractal from “THE” by compressing the “H” into the “T”, then the “E” into the “H”, like this:




Compressed THE (animated)



The compressed “THE” has a unique appearance and is both a letter and a word. Now try a complete sentence, “THE CAT BIT THE RAT”. This is the sentence in stage 1 of the fractalphabet:



And stage 2:



And further stages:





Fractal CAT (b&w animated)


Fractal CAT (color animated)


But, as we saw with “THE” above, that’s not the only fractal you can create from “THE CAT BIT THE RAT”. Here’s what I call a 2-compression of the sentence, where every second letter has been compressed into the letter that precedes it:


THE CAT BIT THE RAT (2-comp color)


THE CAT BIT THE RAT (2-comp b&w)


And here’s a 3-compression of the sentence, where every third letter has been compressed into every second letter, and every second-and-third letter has been compressed into the preceding letter:

THE CAT BIT THE RAT (3-comp color)


THE CAT BIT THE RAT (3-comp b&w)


As you can see above, each word of the original sentence is now a unique single letter of the fractalphabet. Theoretically, there’s no limit to the compression: you could fit every word of a book in the standard Roman alphabet into a single letter of the fractalphabet. Or you could fit an entire book into a single letter of the fractalphabet (with additional symbols for punctuation, which I haven’t bothered with here).

To see what the fractalphabeting of a longer text in the standard Roman alphabet might look like, take the first verse of a poem by A.E. Housman:

On Wenlock Edge the wood’s in trouble;
His forest fleece the Wrekin heaves;
The gale it plies the saplings double,
And thick on Severn snow the leaves. (“Poem XXXI” of A Shropshire Lad, 1896)

The first line looks like this in stage 1 of the fractalphabet:


Here’s stage 2 of the standard fractalphabet, where each letter is divided into smaller copies of itself:


And here’s stage 3 of the standard fractalphabet:


Now examine a colour version of the first line in stage 1 of the fractalphabet:


As with “THE” above, let’s try compressing each second letter into the letter that precedes it:


And here’s a 3-comp of the first line:


Finally, here’s the full first verse of Housman’s poem in 2-comp and 3-comp forms:

On Wenlock Edge the wood’s in trouble;
His forest fleece the Wrekin heaves;
The gale it plies the saplings double,
And thick on Severn snow the leaves. (“Poem XXXI of A Shropshire Lad, 1896)

“On Wenlock Edge” (2-comp)


“On Wenlock Edge” (3-comp)


Appendix

This is a possible lower-case version of the fractalphabet:

Puro Lojo

Los Ojos

He was haunted by eyes. It had begun quite slowly, quite simply: a feeling that he was being watched whenever he went out, that hostile eyes were staring out at him, down on him, from the windows of the town, tracking his progress, feeding the nectar of data to the honeycombs of brains, for savouring later, when he had passed. He started to find quieter, gloomier streets, to stay indoors on sunny days, to keep his curtains drawn. He felt calmer when he knew he wasn’t overlooked, wasn’t being watched, couldn’t be. But then the calm began to evaporate, for he realized that there were eyes even in his house, even here, where he was cocooned in privacy.

The eyes of his books – indeed, the eyes of “books”, the two o’s, the two little eyes staring out between the “b” and the “k”. There were hundreds of eyes, thousands of them, in every book, ready to stare out at him, to watch him, whenever he opened a book and tried to read. Even “eyes” itself, with the twin e’s, seemed to peer at him, if not to stare. It had half-closed lids, ready to open on him, to glare its full. In Spanish, the word opened fully: ojo. The word reminded him of two eyes with a nose between them, with a bindi over the nose, the mystic dot of Hinduism, symbolizing the third eye. In Hindi, though, the word didn’t threaten him: आँख, ānkh. When he’d first started to worry about his books, about the eyes in his books, he’d gone to the public library and spent an hour searching through the dictionaries, making a list of the eye-words he did find threatening, as though he could trap them, confine them, on a single piece of paper.

The “oog” of Dutch. The “öga” of Swedish. The “øje” and “øye” of Danish and Norwegian, which reminded him of the razor-blade slicing the eye in Un Chien Andalou. The “oko” of Czech, Polish, and Russian. The “ojo” of Spanish, the “olho” of Portuguese, the “occhio” of Italian, all from the “oculus” of Latin (“oculo” in the ablative and dative). Then there was the “göz” of Turkish, entirely unrelated, but staring out at him like a cyclops. And what about the “ojú” of Yoruba? It was unrelated to Spanish, but disturbingly similar. Disturbing in a different way was the οφθαλμος, the “ophthalmos”, of ancient Greek. It was such a juicy, gelatinous word, like the juice and jelly of an eye itself, like a mechanism of chemicals and flesh from which the two o’s stared out at him, watching him, judging him, storing data about him for use in his trial, the secret trial that was being prepared for him.

He felt relieved, at first, that modern Greek had a less threatening μάτι, “mati”. But then he discovered that Malay had a word that was very similar, “mata”, though he knew that Malay and Greek were entirely unrelated. He felt his skin prickle as the first hint of a conspiracy trickled into his brain. The lower-case a’s of “matia”, the Greek plural, like the lower-case e’s of “eyes”, were like peering eyes, as though the words were beginning to take on the same form as “ojo” and “oko”, as though they would open fully one day too. He wondered if, one day, all the world’s languages would have eyes in their words for “eye”, would have twin o’s gazing out, glaring out at the reader. The biter bit. The reader read. Or what about a script, a font, a language, that was entirely ocular, entirely based on o’s, that read its readers as they read it? You could do that, could create one. There were enough forms of “o” in the alphabet, or the alphabets, the Latin and French and Czech and Yoruba and Vietnamese.

It was then he realized that he hadn’t looked at the Vietnamese dictionary, having missed it near the end of the shelf. He went to look at it, carrying his eye-list with him. He took the dictionary off the shelf and flicked to the right page. He nearly dropped the book when he saw the word staring up at him: mắt. Like Greek, like Malay. He would discover later, after more research, that the Vietnamese and Malay words probably had a common origin, something he’d half-suspected, after that moment of shock. The language families were spoken in neighbouring regions, after all. But for that moment of shock it had seemed a confirmation of something at work, something beneath the surface, or beneath the lid, peering out, ready to be fully exposed, fully opened, ready to stare its full, to drink his soul.

After his visit to the library, he found it more and more difficult to read English and Spanish, both with eye-like eye-words, both full of o’s. He was haunted by a line from Lovecraft, from “The Shadow over Innsmouth”: “I could not escape the sensation of being watched from ambush on every hand by sly, staring eyes that never shut.” But in English, in Spanish, they were not in ambush. They were there openly, eagerly, greedily. He sought refuge in French and German, whose eye-words were asymmetric, un-eye-like, and where “o” was blessedly far down the list of letter-frequencies. English ran e-t-a-o. All those to’s and of’s and not’s. Spanish was even worse: e-a-o. All those masculine endings, those past tenses, those no’s and lo’s. But French ran e-a-s-i-t-n-r-u-l-o. German was even better: e-n-i-s-t-r-a-d-h-u-g-m-c-l-b-o. He began to sellotape his English and Spanish books shut, as though each were an eye that he was closing by force, blinding so that its myriad inner eyes could not watch him. He felt much calmer reading French and German, much better able to cope when he came across a reference to eyes, and he even laughed aloud when, returning to À Rebours, he read of how the ancestral portraits of des Esseintes alarmaient avec leurs yeux fixes, “startled one with their fixed gaze”.

The disaster, when it came, came without warning. He picked up a French guide to butterflies one afternoon, meaning to browse through it before lunch, and almost at once came across a slip of paper handwritten on both sides. The writing was neat but small and he had to concentrate to read it. It was all part of the trap, he realized too late, to make him focus, to bite more deeply on the poison bait that had been dangled before him. Ice began to form around his viscera as he read, but he could not stop himself until he had finished:

Die einzelnen Worte schwammen um mich; sie gerannen zu Augen die mich anstarrten und in die ich wieder hineinstarren muß: Wirbel sind sie, in die hinabzusehen mich schwindelt, die sich unaufhaltsam drehen und durch die hindurch man ins Leere kommt.

With sick horror, he noted that the passage contained exactly two o’s, near the beginning and near the end, like the grotesque eyes of a distorted, teratomorphic face. Then he turned the slip over and found that the other side contained a translation in English, full of o’s, full of eyes, staring at him, eager to drink the emotion in his face, the realization that he had been trapped. Again, he could not prevent himself from reading to the end:

Single words floated round me; they congealed into eyes that stared at me and that I was forced to stare back into – whirlpools that gave me vertigo and, reeling ceaselessly, led into the void.

He let out an involuntary cry. Where had the slip come from? Who was the author of the German? Who had translated it? Who had written the two languages down, hidden the slip in the book? He looked again and realized that it was his own writing, slow, careful, half-disguised, but unmistakable, now that he looked. There was a conspiracy, yes, there was, and he was the author of it, spinning a web for himself, plotting his own destruction, with hidden motives, hidden hatred. He moaned. Things were moving in his head. The slip was a linguistic key, turning a lock in his subconscious, releasing a phrase that he himself had hidden there. Esse Est Percipi. Berkeley’s great dictum. “To Be Is To Be Perceived”. He knew the truth now. He could not escape, could find no refuge, draw no curtain, close no door, find no darkness to hide in. The universe itself was an eye all around him and he was its eternal focus, naked always, visible always, pierced through and through by a torturer’s gaze that created its own object of torture.