Over the years I have worked on many different research and computing projects, all over the world. Most of my scientific work is related to the origin of life, evolution, and complex systems & emergence. Below is a brief overview of the main projects that I am currently working on. Preprints of my publications on this work are available for download (see the list of publications).

Relevant references

Below are a few relevant references related to the research projects described on this page.

Chasing the tail: The emergence of autocatalytic networks
W. Hordijk and M. Steel
BioSystems 152:1-10, 2017

The living set
W. Hordijk
The Scientist, 1 June 2015

The EvCA project: A brief history
W. Hordijk
Complexity 18(5):15-19, 2013.

Complexity by subtraction
D. W. McShea and W. Hordijk
Evolutionary Biology 40(4):504-520, 2013.

Spontaneous spirals
W. Hordijk
Plus magazine, 22 December 2016.


Having worked on so many projects over the years, it is impossible to list all of my collaborators. But here are a few people who have definitely had a major impact on my science & thinking.

Mike Steel: My main collaborator on autocatalytic sets. We have been working together for more than 10 years now, and it's been a great pleasure!

Stuart Kauffman: The originator of the concept of autocatalytic sets, and still an active collaborator. It's an honor to be working so closely with him.

Melanie Mitchell: One of my (former) PhD advisors in the EvCA group at SFI. A wonderful teacher and science popularizer.

Jim Crutchfield: My other (former) PhD advisor in the EvCA group at SFI. A great inspiration and example.

I believe in Spinoza's God who reveals himself in the orderly harmony of what exists, not in a God who concerns himself with the fates and actions of human beings.
   --- Albert Einstein


Autocatalytic Sets and Origin of Life

An autocatalytic set is a self-sustaining chemical reaction network in which the molecules mutually catalyze each other's formation from a basic food source. They are believed to be an underlying principle of all living systems, and also to have played an important role in the origin of life. We have developed a formal framework of autocatalytic sets, called RAF theory, and used it to study the probability of existence and the structure of autocatalytic sets in a simple polymer model of chemical reaction networks. Furthermore, we have applied the formal framework to study experimental chemical examples of autocatalytic sets, and to show that the metabolic network of E. coli forms a large autocatalytic set.

Current work continues our mathematical and computational investigations, but also focuses on bringing theory and experiments closer together. An increasingly large network of collaborations is developing around the general concept of autocatalytic sets, including chemists, biologists, mathematicians, computer scientists, physicists, and even philosophers. Our hope is that, eventually, this work will provide detailed insights into the origin and early evolution of life.

Evolution of Emergent Computation

In the Evolving Cellular Automata (EvCA) project, a genetic algorithm was used to evolve cellular automata to perform certain non-trivial computational tasks, in an effort to gain more insight into the question: "How does evolution produce sophisticated emergent computation in decentralized systems composed of simple components limited to local interactions?" A cellular automaton is a simple model of a decentralized system with only local interactions, and a genetic algorithm can be used as a simple model of an evolutionary process.

The results of the EvCA project have provided much insight into the evolution of emergent computation in cellular automata. As a graduate student I was part of this project, which was mostly based at the Santa Fe Insitute (SFI). I still regularly use this versatile modeling framework to study additional phenomena in evolution, such as how representations come about, or the notions of "complexity by subtraction" or "evolution of evolvability".

Spontaneous Spirals

Natural systems such as the slime mold Dictyostelium discoideum and the Belousov–Zhabotinsky reaction show beautiful spiral waves in their dynamical behavior. However, these global patterns arise spontaneously from only local interaction between individual amoeba or chemicals. How does this happen?

We have developed a simulation model, implemented as a cellular automaton, to reproduce and study such spiral wave formation. These patterns appear over a range of model parameter values, seem robust against noise, and regenerate quite accurately the dynamics as observed in the actual natural systems. This model, known as ISCAM, therefore provides a simple and useful tool to study this phenomenon. Although the model itself was already developed several years ago, some of the work is still ongoing.


There are many other projects I have worked on over the years, related to cellular automata, genetic algorithms & fitness landscapes, algorithms for phylogenetic tree reconstruction, species distribution modeling, simulating chemical reaction networks, modeling foraging behavior, teaching evolutionary algorithms, general computing support, high performance computing, and so on. Too many to list in detail here...