Professor Henrik Jeldtoft Jensen  -  Complex Systems Science

Department of Mathematics 
Imperial College London
South Kensington campus
London SW7 2AZ 
Office: Electrical Engineering Building - EEE1201 
Tel: +44 (0) 20 759 49853,
Fax: +44(0) 20 7594 8517




              For Imperial College Centre for Complexity Science  click here

  Why do we do science?

  For the same reason as Glenn Gould plays piano:

   The purpose of art is not the release of 

   a momentary ejection of adrenaline but
   rather the gradual, lifelong construction of 

   a state of wonder.

                                         Glenn Gould

  There are no such things as
  applied sciences,
  only applications of science. 

                                         Louis Pasteur

  We shall not cease frome exploration
  And the end of all our exploration

  Will be to arrive where we started
  And know the place for the first time.
           T S Eliot                 



On the relationship between  painting and art  

Mathematics is painting without the brush; painting is mathematics without the chalk.
          Mathematics and Painting.  Article first published in 
           Interdisciplinary Science Reviews
, 27, 45 (2002).
Music and painting

   Two videos with
   music composed by Eitan Altman
   and paintings by Henrik Jeldtoft Jensen

  Watercolour   and   Acrylic


      Oxherding - HJJ08

 An essay on the true emergent nature of time 

 Sindsvaesner og tidens egentlige natur   (in Danish)

Visions for Complexity Microsoft Word - versio2 taronja

Theory of complexity: interconnectedness, emergence and hierarchical structure.

Talk at the Opening of the Complexity Hub Vienna – 23 May 2016


Feza Gursey Institute and Imperial College International Summer School and Research Workshop on Complexity
  Istanbul 5-10 September 2011       

   For more information click here                                    



  Download my lectures a the school: Dynamics of Complex Systems and Music and the Brain


 Complex Systems:

  I lead the Centre for Complexity Science  (additional information here)
The Centre engages in a range of research into the applied and fundamental aspects of complexity science, where often the most interesting questions extend beyond the realms of idealised models and the simplifications arising within typical experiments. To access and begin to address such questions, theoretical investigations are often best carried out in close collaboration with researchers working on a variety of real systems.

This is a common theme within the Centre; much of the research exploits the richness of real world data sets in order to study fundamental questions in complexity science. Many projects undertaken are collaborative in nature, and a diverse range of research is currently being undertaken within this framework, including:

applying evolutionary dynamics to study economics and finance
exploiting ideas from statistical mechanics to analyse the dynamics and structuring of social insects
applying themes from self-organised criticality to analyse heart arrhythmia
employing field theoretic methods to improve our understanding of the statistical mechanics of complex systems

Ultimately, the focus is on maintaining a diverse set of research themes within the Centre which allow for extensive insight into real world data, and the opportunity to identify commonalities of theoretical and practical importance to fundamental complexity science.

 Complexity, collective effects, and modelling of ecosystems:  
formation, function, and instability

       Paper in the Annals of the New York Academy of Sciences 


  • The complexity approach realises that properties at system level consist of interaction induced co-operative emergence: interacting components lead to hierarchical structures with different causations at different levels.

  • Complexity realises that a multiple-component system evolves and adapts as a consequence of its internal and external dynamical interaction. The system keeps becoming a different system. The demarcation between the system and its surroundings evolves.

  • Complexity bridges the gap between the individual and the collective: from psychology to sociology, from organism to ecosystems, from genes to protein networks, from atoms to materials, from the PC to the World Wide Web, from the citizens to the society.

  • When a multiple-component system is manipulated it reacts by feedback. The manipulator and the complex systems will inevitably become entangled: the farmer harvests as he sows and nurtures. Complexity research attempts to understand the sum of the multiple causes. 
The hierarchy of order

For me statistical mechanics is about understanding why the whole is different from the sum of the parts: identifying and understanding emergent properties; understanding how the combined effect of simple interactions and many degrees of freedom creates the never ending complexity we observe in our surroundings. Obviously these general questions have to be studied through concrete cases. I am fortunate to work together with a number of graduate students, research assistants and colleagues on research projects including biology, neuroscience and statistical mechanics.

The analysis of the emergence of structure in networks is a natural tool in this quest.

Here follows a brief description of some of our research
  Tangled Nature: Ecology and Economics

Evolutionary ecology is a prototype example of dynamics of complex systems. We have developed a simple individual based model which exhibit intermittency and is able to reproduce a range of ecological observables such as the species-area law and typical species abundance distributions.                                                                                                             

Click here for an overview poster on the properties of the   Tangled Nature Model.
Below are a few preprints

          Review to appear in the proceeding of the 2006 ECMTB Dresden meeting

          The Tangled nature model with inheritance and constraint: Evolutionary ecology restricted by a conserved resource 

More recently we have developed the Tangled Nature approach to study economics
           Entangled economy: An ecosystems approach to modeling systemic level dynamics

and some reprints: 
          Diversity as a product of interspecial interactions
         The species-area relationship and evolutio
         Network properties, species abundance and evolution in a model of evolutionary ecology.
         Tangled Nature: a model of evolutionary ecology. (J. Theo. Biol.)
       Time dependent extinction rate and species abundance in the Tangled Nature model of biological evolution. (Phys. Rev. E.)   
       The Tangled Nature model as an evolving quasi-species model. (J. Phys. A)

On selection of the mode of evolution
        Origins of evolution: Non-acquired characters dominates over acquired characters in changing environment

   Record dynamics:
Intermittency and relaxation is very often encountered in complex systems. In a broad range of cases we have found that log-Poisson record dynamics is a good description of the observed dynamics. This has a number of very strong implications concerning the structure of the phase space as well as many consequences for the macroscopic temporal behaviour.

        Evolution in Complex Systems (Complexity).
        Intermittency, aging and extremal fluctuations.
        Record dynamics and the observed temperature plateau in the magnetic creep-rate of type II superconductors.

  Statistical Mechanics of epedemics:

       We have studied the fluctuations in sizes of
        Measles Outbreak in a Population with Declining Vaccine Uptake  SCIENCE 301, 804 (2003)
                additional material:  click here

        and used lattice models in the study

       On the critical behaviour of simple epidemics,
                                            Proc. Rol. Soc. Lond. B  264, 1639 (1997). pdf


   Population dynamics and evolutionary dynamics:

Investigations of how the microscopic behaviour of the individuals in a population affects the behaviour of the whole.  Through the eyes of statistical physics, our main emphasis has been on the phase transitions that occur in our model as the population becomes extinct. Of particular interest is our recent study of the nature of the extinction transition in fractal dimensions between one and two. Aside from this largely theoretical approach, we also examine how the model could be used for ecological purposes, particularly in the conservation of species.

The clustering in type space and its relation to neutral and non-neutral models.

  Modelling in creativity and music cognition using a complexity science approach:

We explore patterns in brain activity that are a result of a musician's playing. The focus in particular is to elucidate what happens when creative leaps and ingenuity occur during this playing - EEG recordings are analysed. Together with Conductor Richard Dickens and J Bhattacharya, Goldsmith.

   Brain scales

         We analyse the spatial and temporal scales of the brain by use of fMRI.  

Additional interests: Kids, books, music, philosophy, painting,.... 
List of publications:

   Click here to see Publication List


 Some lectures:

    Emergence of complex structure through co-evolution:
    The Tangled Nature model of evoultionary ecology
Key note lecture at the French Complex systems Societry Meeting,
       Paris 25-27 Nov. 2009)
Slides  (8.5MB)

    On the relation between painting and mathematics.
    (Key note lecture at the conference on Excellence: Education & Human Development,
      Athens, 1-4 July 2009.
     Slides (39.1MB)

   Tangled Nature: a model of evolutionary ecology.
     Slides  (2.9MB)

    Dynamics of complex systems: The record dynamics.
Slides  (2.2MB)

     Subtle relations: 
     prime numbers, complex functions, energy levels and Riemann.
      Slides  (1.0MB)

   Self-Organised Criticality:what does it mean and is it important.
     Slides (1.1MB)

    Godel's  Proof.
    An introduction to the back ground, the structure of the proof and its consequences.
   Slides (1.0MB)


Some selected publications:
Complex systems:
  •  Self-Organized Criticality, H.J. Jensen, Cambridge University Press. 1998. 
         Buy online from  Cambridge University Press or from
  • Anisotropy and universality: the Oslo model, the rice pile experiment  and the quenched Edwards-Wilkinson equation,
        G. Pruessner and H.J. Jensen, Phys. Rev. Lett. 91, 244303 (2003). pdf
  •  A solvable non-conservative model of Self-Organised Criticality,
         G. Pruessner and H.J. Jensen, Europhys. Lett. 58, 250 (2002). pdf
  •  Universal fluctuations in correlated systems,
       S.T. Bramwell, K. Christensen, J.-Y. Fortin, P.C.W. Holdsworth,
        H.J. Jensen, S. Lise, J. Lopez, M. Nicodemi, J.-F. Pinton, M. Sellito,
       Phys. Rev. Lett. 84 , 3744 (2000).  pdf


  • Emergence of species and punctuated equilibrium in the Tangled Nature model of biological evolution.
        H.J. Jensen, Physica A: 340,  697-704 (2004). pdf
  • Darwinian selection in a locally unstable Boolean Network.
        D. Eriksson and H.J. Jensen, J Stat. Mech.: Theor. Exp. P09001 (2004).pdf
  • Nonequlibrium Roughening transition in a Simple Model of Fungal Growth in 1+1 Dimensions,
     J.M. Lopez and H.J. Jensen, Phys. Rev. Lett. 81 , 1734 (1998). pdf
  • A Genric Model of Morphological Changes in Growing Colonies of Fungi,
     J.M. Lopez and H.J. Jensen,  Phys. Rev. E. 65, 021903 (2002). pdf


Vortex dynamics:
  • Time dependent phenomena in transport properties and I-V characteristics of a model for driven vortex matter.
         M. Nicodemi and H.J. Jensen, J. Phys.: Cond. Mat. 16, 6789 (2004). pdf
  • Creep of superconducting vortices in the limit of vanishing temperature A finger print off equilibrium dynamcs,
     M. Nicodemi and H.J. Jensen,  Phys. Rev. Lett. 86, 4378 (2001). pdf
  • Aging and memory phenomena in magnetic and transport properties of vortex matter,
     M. Nicodemi and H.J. Jensen, J. Phys. A 34, 8425 (2001). pdf
  • Off equilibrium glassy properties of vortex creep in superconductors,
       H.J. Jensen and M. Nicodemi, Europhysics Lett. 54, 566 (2001). pdf
Other topics:
  • Mathematics and painting.
       H.J. Jensen, Interdisciplinary Science Review 27, 45 (2002). pdf
  • Mathematical Moddeling of Species formation.
        K. Christensen and H.J. Jensen, Science Progress 83, 93 (2000).  pdf

Last update  20.7.14