The Hilbert curve Christianopolis


Johannes Valentinus Andreae proposed his vision for a Utopian Christian city to be Christianopolis.

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Concentric square rings of the city centre around the chapel. From the centre follow the ring of the college, two residential rings and the ring of industry. Each is in a way a step in a hierarchy towards higher spiritual meaning – the hierarchy of priorities for a society based around faith. The way that hierarchies work in general is that each step is made up of an independent member, fulfilling their role. Yet in this hierarchy each step cannot exist without any one of the others, they all make up a single whole – the single whole of life. The divisions are necessary for the unity. The borders are necessary to transfer value from one component of the city to the other and contribute to its unity.

Each of the concentric rings are fully self sustainable in their function. All that is needed during the work day is accommodated in the ‘industry ring’. All that is needed for study is accommodated in the college ring and the accommodation rings provide everything for domestic life. This integration of categorised services means that the streets between the rings are only there to support the idea of the territory of the city, without serving any function in themselves.

So what could a city that is at once divided and yet united – a city that embraces its borders – yet is not based around a religious ideology – look like?

I like the idea of city functions based around a continuos line. For this I looked at space filling curves and in particular the Hilbert curve.

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It works as a single line that fills a shape – a square – and makes spaces within that square by folding/turning. To make the implications of this in a city context as clear as possible I like to think of it as an extended border between France and Switzerland at the Novartis site. By moving between the cavernous spaces, one would be crossing the line – in effect crossing the border between France and Switzerland back and forth – yet never really entering either country, since they would stay within the confines of the square [the boundary of the space that the line fills].

At the moment I am making a collage of what a ‘Hilbert curve city’ might look like. Just as in Christianopolis, buildings with a certain function follow a line. Yet since this is a city that is not centred around an ideology, the lines are not concentric, but continuous. To make the streets work, they need to periodically cut across this continuous line of buildings. At these points a citizen travelling along a street has to come to terms with whatever building programme cuts their path. If its a supermarket they travel though it to the back exit, it could be an arcade, a shopping mall, perhaps a shop or a cafe. The citizen is enriched by and enriches the built programme of the city as they travel along the street. These crossing points are somewhere in-between the exterior and the interior, just as the spaces I highlighted to be the ‘interiorised public spaces’ of modern cities.

At the moment the collage looks like this and is to be updated throughout the evening:

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One Response to The Hilbert curve Christianopolis

  1. Sabrina Morreale says:

    Why are you working with 2d images flat onto this ‘Hilbert curve? Would not be maybe more productive to work with possible fragments/pictures or videos from the Novartis centre, cutting them in pieces and constructing the curved world?