Images from various projects - some of them from research projects, some from work projects, and some just for fun.
Click on the thumbnails to to see the larger versions of the images.
- Accumulated movement - Part of a demo made for artist Mikael Lundberg's
Telefonplan proposal (the proposal won the competition).
A fixed camera was used to record material for about six hours, and I wrote a program to accumulate the
differences from one frame to the next. Portions of the fixed view where there is a lot of activity (e.g. where
many people like to walk) will accumulate a lot of movemeent, and in that way creating paths in the image.
Movies of the accumulated movement are also available on this site.
Accumulated movement from two four minute long periods of time.
Accumulated movement over six hours.
- GPS data processing and programming for artist Mikael Lundberg's project
Mikael wore a GPS unit for approximately 18 months in 2002 and 2003, collecting a large data set. The data set was then visualized in two ways.
A book was made with tracks from movement from one day per page. The second visualization of the data is a
movie that show Mikael's movement (The link target is only a small fragment of
the movie, and is hosted at Mikael's site.) at a greatly accellerated rate. "Lifeline" was later sold to the museum of modern art in Stockholm.
- Random Lotka-Volterra networks
A discrete time version of the model. Coordinates for the plotted points are formed by taking the length of the state vector in three consequtive steps.
A continuous time version of the model. The plot is a phase diagram of the two dominant components.
- Basins of attraction for a system with a pendulum and two magnets.
The pendulum is attracted by the magnets, and the movement of the pendulum is also damped.
The damping will cause the pendulum to slow down over time and the pendulum will eventually come
to rest by one of the magnets. Points that are colored red in the images correspond to initial
conditions where the pendulum comes to rest by the left magnet, while blue points correspond to
initial conditions where the pendulum comes to rest by the right magnet. This is an example of
a chaotic system.
A java simulation of this chaotic system (and some additional information)
is also available on this site.
- A Gray-Scott reaction-diffusion system - an example of a mechanism for
pattern formation (morphogenesis). This reaction-diffusion system can generate a wide variety of patterns,
for example self-replicating spots, spiral waves and labyrinths.
- Random rhombus tilings (Joakim Linde, Cristopher Moore and Mats G. Nordahl (2001),
Generalization of the Rhombus Tiling, Discrete Mathematics and Theoretical
Computer Science Proceedings AA, pp. 23-42.)
The 2D rhombus tilings can be seen as three-dimensional boxes stacked in a corner and projected
down to two dimensions.
The heights of the stacks of boxes are actually very useful, as they provide
a height function, which may serve as a representation of particular tiling configurations
and is also highly useful for theoretical reasons. Height functions also exists for many other
A random lozenge tiling (2D rhombus tiling) created with the
Coupling from the Past (CFTP) algorithm.
The same tiling, but with the frozen tiles removed. An example of an
"Arctic circle" phenomenon.
The outer shell of the 3D rhombus tiling is a rhombic dodecahedron.
Analogous to the 2D case, the 3D rhombus tiling may be viewed as stacked four-dimensional boxes projected
down to three dimensions, although this requires a bit more effort to wrap your head around.
The outer shell of a 3D rhombus tiling.
The unfrozen tiles in a random 3D rhombus tiling created with CFTP.
Wireframe of a random 3D rhombus tiling created with CFTP.
- Random 3-coloring (AKA 3-state antiferromagnetic Potts model at zero temperature) of the square lattice
A random 3-coloring created with CFTP.
The same 3-coloring, but with the frozen region removed. The border appear to be approximately circular. Example of
an "Arctic circle" phenomenon.
- Random 3-coloring (AKA 3-state antiferromagnetic Potts model at zero temperature) of the cubic lattice
Center slize of 3-coloring created with CFTP.
The unfrozen region of a random 3-coloring.
The unfrozen region of a random 3-coloring with a more restrictive boundary condition.
- Viscous fingering
Viscous fingering is a process where a less viscous substance displaces a more viscous one, and this creates
complicated branching patterns.
This particular example of viscous fingering was made using a layer of thick paint between two transparencies.
After the paint had been applied the transparencies were quickly pulled apart (from bottom to top in the image) and when
the paint had dried the transparency was scanned in order to produce the image above. By varying the amount of pigment mixed
into the paint it is possible to vary the thickness of the paint. Varying the amount and thickness of the paint produces different types
of fingering patterns.
- SMS for the Cube.
The Cube (Kuben) is part of the swedish millenium monument (Milleniemonumentet) in Göteborg. Four computer controlled video
projectors can display video on the four vertical faces of the cube. The photo above show one of the installations that has
run on the Cube. While that installation ran it was possible to use cell phones to send SMS to the Cube, and the messages would
then be displayed on the Cube for a while.
Sadly no part of the millenium monument is active now, due to lack of funding.
Update 2012: The cube was dismantled earlier this year. It is supposed to move to another location,
and I will be plesantly surprised if that actually happens.
- Photos from a RoboSumo comptition
Photos from a Lego Mindstorms RoboSumo competition held for students at the IT-university's Intelligent Systems Design program in 2002.
The matches took place on a raised platform with a dark border. The dark border makes it possible to use a light sensor to figure out if a
robot is close to the edge. All robots were required to have a lamp at the highest point turned on. In this way it was possible for the
robots to find each other by using a light sensor.
- Photos from two RoboRace comptitions
Photos from two Lego Mindstorms RoboRace competitions held for students at the IT-university's Art&Technology program.
Clicking on either thumbnail will take you to the corresponding photo gallery.
The race track has a dark border, which means the robots can use a light sensor to determine if it is close to
the edge of the track. Races were run in pairs in opposite directions so that the competing robots would have to meet
at some point of the narrow track.
- Simulated stigmergy.
"Wasps" (represented as yellow squares) move about randomly. When a "wasp's" local environment matches
one of the building rules a hexagonal cell is desposited in the current location. With a suitable set of building
rules very complex structures can be built, with very simple agents and without central planning or a blueprint.