Fractal Cities


Humans are very inefficient drivers, and cities are built with a square based grid that forces the intersection of perpendicular paths. Mix these two facts together and you get the traffic we all hate today. Traffic is not only a waste of resources (time and fuel), it is dangerous and makes people behave irrationally (road rage).

There are two ways to fix this. Remove humans from the equation, or remove the intersections. Google and others have already created autonomous vehicles, with outstanding safety records. This article looks at the infrastructure problem. Without a doubt, given the enormous and static infrastructure we inheritted, the autonomous vehicle is the preffered transportation solution moving into the 21st Century. Remove the internal combustion engines from vehicles and we have a sustainable, clean, safe, and efficient means of ground based transportation for our civilization.

I set out to find what would happen if I used a fractal equation to design cities. I wanted a city structure built around the personal automobile and transportation network.  I want to eliminate the crossing paths of commuters to reduce the time spent waiting.

First of all, 'Fractals' refer to a type of geometry where a very simple equation produces an infinitely complex geometric figure.  'Infinitely complex' means that no matter how many times you zoom into a fractal image you will always see new results - forever and ever.  Fractals have more possibilities built into them than the number of atoms in the entire universe.

Fractal geometry explains a lot of natural structures and produces images that humans find beautiful.  Incredible images can be created with simple equations:
The picture above was made by applying a very simple rule such as z = z^2 + C many, many times.

I am convinced fractal geometry is a fundamental driver of the shape of the universe.  It appears to be the math that most biological structures follow.  It explains the structure of our bodies and fits with the idea that DNA is the 'code' that our bodies were built around. It may be God's geometry...

To be clear, when applying fractals to cities I am not interested in zooming in forever and ever, I have a smallest unit I care about - which is a city block.  The fractal will actually grow out of this, more like a tree in how it starts at the trunk and expands outward.


Fractals work by applying a simple rule over and over again.  The rule I started with to design a city grid was based on transportation:

1. Roads may only intersect at 120 degree angles relative to each other.
To eliminate the need for traffic lights and stop signs I implemented the follow rule:

2. If more than 1000 cars per hour enter an intersection from any direction the roads must be elevated such that no turns intersect with each other.
Left turns are on 3 different levels. One lane is dug into the ground, one stays at ground level, and the third is raised.


The interesting thing about fractals is the repetition of features regardless of scale.  Lets start by looking at a typical suburban neighborhood.
Suburban neighborhood intersection.  Roads arelarge enough to park on each side of the street.  (Grey blocks represent home footprints)
This intersection allows for great visibility and requires only that someone making a left turn yield to other cars making a left turn before him.  No stop signs needed.

Notice that every car has exactly 2 options when they approach the intersection:  left or right.  This is always the only choice you have to make, no matter whether you are on an 8 lane free way or in a suburban neighborhood.  In every intersection in the entire city there is no need for stop signs or light signals. This means that traffic will always flow at its most efficient rate under the given conditions.

The next larger scale of intersection after the suburban neighborhood looks likes this:
Standard intersection for roads with more than 1000 cars per hour.
Continue the scale up of roads so that as traffic loads increase the number of lanes increase, maintaining the same elevation structure as shown.

The following is the first major city district designed with this method.  There are hexagons within hexagons that make up this district. The darker colored regions are suburban neighborhoods, while the more sparse hexagons are apartments and offices.

When you look at the image above it probably reminds you more of the inside of a beehive than a city - because your conception of a city likely invokes square buildings on square grids.  Nothing in nature makes square homes!  Why should we?

Questions Remaining