Other than existing entirely in halfgray tones never quite reaching black or white — those absolutes approached the closest by the shimmering black disk of the sun and the eigengrau-tinted whiteness of the homogeneous sky — the place he called Mandelbrot City was photorealistic at every level of detail: streets looked like streets, doors like doors, and so on. It was at the infinitely bisectable boundaries between the scales where the maps twisted (still twist) along some unrepresentable dimension without losing continuity. He could, and did, stop on a sidewalk to peer through the window of an empty store and then look away and keep walking without seeing anything wrong at any moment yet walking, afterwards, on a different empty sidewalk than the one he had stopped on. It had at first seemed to him a software error (or, worse and dizzying, less a bug of the code than a feature of the mathematics of which the code was a brazen shanzhai) but he understood its para-cartographic possibilities as soon as he looked away from the problem into something else and then looked back to it to see it changed.
This realization came late during the development of his program and of the psychiatric difficulties that drove it. His original plan had been filled with the naivete of the professional artist: to perform the cheapest plot of fictional self-therapy by building a virtual city isomorphic to the one in his dreams and then force a catharsis by destroying it before its oniric original, or rather the intolerably cliched invisible thing that chased him every night, caught up him with consequences he feared with irrational certainty would be more than symbolic. His discovery of the peculiar topology of Mandelbrot City pointed to an alternative approach better suited to his natural cowardice. There had to be, he saw, an urban configuration — small room or monumental piazza — made so utterly safe by a simple reversal of the unspecifiable factors that made some places ominous that by conditioning his mind to dream himself in them he would be protected from the pursuer that was echo and agent of the increasingly anomalous functionality of his brain.
It's important to understand that he was right about this. Such urban configurations exist, invaluable because none would voluntarily trade away one. Some cultures in potential spaces — advanced enough to thrive without needing to interact with the always dangerous planes of actuality — have nestled their civilizations inside immense cities built in such patterns to protect themselves from dangers not describable without risk. Had he reached such a place he wouldn't have died. It's also true that some of those configurations were accessible from any of the places in Mandelbrot City he found himself in when he put on his wraparound glasses in those rare occasions when he had taken them off. The right combination of attention and movement, turning around a corner while watching the top of a building, closing his eyes as he walked around a fountain, would have led him gradually to a place safe even from his own brain.
The topology of Mandelbrot City made it possible to find them: what to an external observer would have seemed random actions had their own internal necessity. Soon, in his moments in the virtual city, which came to be identical with those when he was not dreaming himself in a different city being chased by his own death, he was moving across entire architectonic styles and urbanistic theories with the ease with which one crosses a quiet street. The alien neighborhoods did not faze but rather spurred him. He could not imagine what a safe place could look like. By impeccable necessity it would only be found far from the imaginable streets where he had begun.
There are narratively plausible stories in which he is lost forever in those streets, either before or after being caught by what was pursuing him in his dreams; or some suitably ironic event in the real city kills him (the least likely option, as it would have necessitated for him to ever leave his house).
In or adjacent to reality his death was still overdetermined but came from an angle orthogonal to and even stranger than the one that structured the city. He was killed still relatively far from the claws of his pursuer by the inhabitants of one of the precious safe places that, although could not be walled against those seeking sanctuary, could still destroy them as they approached; not to prevent a refugee from bringing something dangerous to a place where such a thing is by definition impossible but, by a logic common to every being capable of imagining a city, to avoid sharing this safety with somebody else. Similar dangers attend those who seek those places of safety through the superficially different artistic forms of religion, literature, etc.