It happened that one late night as I was reading a collection of poems I was called on by a most peculiar creature. As it entered my hall, (I cannot call it either a man or woman, as we shall see) I was immediately most horrified and I jumped back in fright at the sight of a hideously twisted and irregular figure.
"Out! Out!" I cried to the aberration, and I started after it. It made quickly for my study, and a small chase through the house ensued, during all of which it insisted in a crackled, confusing voice that it was a visitor from a fall-off land wishing only to speak to me. Of course I knew that such an aberration could be nothing but a criminal of the worst kind, come to bring harm to myself and my family. The chase slowly came to a halt, my facilities of body not being what they were in my youth, and we rested, panting, on either side of the Men's door. It was in its stillness that I was finally able to get a clear look at it, or should I say I was able to notice that what I had been seeing was anything but a clear look.
Its figure was as if that of a line, a woman, but contorted and redoubled in such a way that even the most beastly of women could not achieve, to the point that it almost resembled a man, though its form was so indecipherable that he could not be a figure at all. The longer I looked at its bizarre intricacies, the less I seemed to see it; I could not assemble a clear picture of its shape, for, to my eyes, it appeared to be a form which was neither line nor polygon. I accused it at once of being a witch, of practicing black magic which made me to believe I was seeing something which simply could not be. Before I could finish my accusation, though, my voice trailed off in further confusion as I began to perceive amongst the ugliness of its twists and kinks a certain bizarre order, as if its own composition was, in fact, a series of images of itself of lesser and lesser magnitude.
With this observation my anger subsided and I was filled with curiosity. How could this be, this creature inside itself? I broke the silence which had arisen in our exhaustion.
"What are you, curious invader?"
"I, sir," it responded timidly, "am a Fractal, an accidental visitor from a foreign land far to the north."
"What do you mean, by this word 'fractal?' To me, you appear as if to be a creature inside itself, a strange multiplication of yourself."
"Indeed, the people of my land are all possessed of what is called 'self-similarity,' so that any small portion of my shape is but a tiny copy of the entirety of my form."
"So you are like the women of our land, who, if cut in two, as the flashy magicians purport to do, resemble nothing more than two smaller copies of their entire selves."
"Not so, for, as you see, I am not a simple line without curve."
"Then you are like the men of our land, say, a Triangle, which could, if one were to be so cruel, be divided into four, or sixteen, or sixty-four smaller copies."
"Again, you are mistaken, for, as you see, I haven't any of what you call an 'interior.'"
"This is true," I replied, and trying very hard to comprehend this creature, asked, "so you are not a being of one dimension?"
"And you are not a being of two dimensions."
"What else can there be?"
"I come from a world of a dimensionality between one and two," it said.
"Preposterous!" I cried, and again shouted for it to leave my home, convinced once more that magic was clouding my vision.
When it had left my home, I returned to my study of poetry, assured that such a hideous thing would soon be apprehended by the police and done away with.