My talk given at the "Fractals 2000 in Biology and Medicine" symposium in Ascona, Switzerland, on March 11, 2000. That paper explains why the (very high) fractal dimension of Western Europe's coastline should be considered as one of the main factors driving its long term evolution, following my theory of science exposed in The Secret of the West (1997, 2007).
---The symposium "Fractals 2000 in Biology and Medicine", 07-11 March 2000, Ascona, Ticino (Switzerland) (program).
Safety copy of internet version July 2000. Source.

---The paper as published in the symposium collected papers in May 2002. PDF doc. Smartphone version.
(D.Cosandey: "The Fractal Dimension of the Coastline as a Determinant of Western Leadership in Science and Technology" dans G.Losa, D.Merlini, T.Nonnenmacher, E.Weibel: Fractals in Biology and Medicine, Volume III, Birkhauser, Basel, Boston, Berlin, May 2002, p. 319-324).
Theory of Science


Promotional webpage for the symposium "Fractals 2000 in Biology and Medicine", in Ascona, Switzerland (8-11 Mar 2000).

Symposium Venue

The Symposium wil be held at the Centro Seminariale Monte Verità, CH-6612 Ascona, TI (near Locarno), Switzerland Ascona and the Monte Verità can be reached directly from Lugano-Agno airport, by train or car through Locarno.
Telephone: 0041-91-791 01 81
Fax: 0041-91-780-51 35
E-mail: reception@csf-mv.ti-edu
Detailed information on Website:

(Click the images to enlarge)
Arrival:Tuesday 7, March 2000
Departure:Sunday 12, March 2000

Scientific Goal

The main goals of the Third International Symosium will be: first, to explore the potential that fractal geometry offers for elucidating and explaining the complex made-up of cells, tissues and biological organisms either in normal, abnormal and tumoral conditions. Second, to develop the concepts, questions and methods required in research on fractal biology and natural and cultural phenomena and to evidence the pitfalls of a too simplistic application of these principles in investigating topical subjects of biology and medicine.

It aims to bridge the communication gap between various disciplines, to discuss present and future applications of the fractal geometry, by bringing together cellular, molecular and natural biologists, engineers, mathematicians, physicists, physicians and other scientists in an ambient favouring the interdisciplinary vision.

The Symposium might be relevant for the industry involved in developping and applying softwares and methods in the fields of morphometry, quantitative image analysis, stereology, nonlinear dynamics and related topics. Industrial researchers are invited to submit papers for regular platform or poster sessions.

Young participants would benefit from attending not only by listening lectures presented by invited scientists but also by presenting their current research during platform or poster communications so that the exchange of informations and ideas between different groups of researchers working in different areas of science and attracted by the fractal paradigm, will be strengthened. They are strongly encouraged to deliver a manuscript to be included in the Conference Proceedings which will be published in the new series " Mathematics and Biosciences in Interaction " by the Birkhäuser Press, Basel, Boston, Berlin.

Symposium Themes

Eight coherent sessions will be scheduled and tentatively headed as:
  • Fractals (spatial and temporal), power law, nonlinear dynamics, complexity, self-organization and chaos in metabolic and signalling pathways, in biodegradation and in natural environment
  • Fractals in biological design, angiogenesis, evolutionary pattern, morphogenesis, spatio-temporal tree structures, vessel branching
  • Fractal structures, functional complexity and chaos in tumours
  • Fractals in nuclei (DNA/ chromatin organization), gene expression, membranes and cell organelles during growth and death (apoptosis, necrosis)
  • Fractal in connective tissue, epithelial-stromal tissue interface, tissue-remodeling, biopolymers
  • Fractals in pathologic states of brain, nervous and cardiac tissue
  • Fractals of immunologic response and in autoimmune, aging and chronic diseases
  • Fractals in biomedical engineering,pattern recognition,radiological, sonographic and ultrasonic image analysis


The four-days symposium will be organized in morning sessions that will be devoted to lectures given by invited speakers on main topics and to shorter contributions (20 min.). Afternoon sessions will be devoted to free platform communications (20 min.) and poster sessions selected among submitted abstracts.

Posters session
Will be organized in the Balint Hall on wednesday and friday afternoons. Posters will be left displayed during the all symposium.

S.Albeverio (Germany), A.Brù (Spain), M.Buiatti (Italy), N.Dioguardi (Italy), A. Einstein (U.S.A.), G.Landini (UK), Hirato Kitaoka (Japan), G.A.Losa (Switzerland), B.Mandelbrot (U.S.A.), T.Mattfeld (Germany), D.Merlini (Switzerland), E.Oczeretko (Poland), T.F.Nonnenmacher (Germany), L.Nottale (France), J.P.Rigaut (France), B.Sapoval (France), P.Walizewski (Poland), E.R.Weibel (Switzerland), B.West (U.S.A.)


Tuesday 7

6pm-10pm: arrival/registration

Wednesday 8

9am: late registration


9.30am: SESSION I: Chairman: T.Nonnenmacher

9.30 B.West
10.15 M.Meyer
10.40 B.Sapoval
11.05 Break
11.25 H.Kitaoka
11.50 H.Kitaoka
12.15 P.Delsanto
12.40 G.Baumann

1 - 3 pm: LUNCH

3 pm: SESSION 2: Chairman: B.Sapoval

3.00 F.Nekka
3.25 J.Konarski
3.50 C.Felgueiras
4.15 N.Südland
4.40 D.Merlini
5.00 N.Sala
5.20 S.Albeverio

8 pm: DINNER

Thursday 9

9.30 am: SESSION 3: Chairman: B.West

9.30 G.Landini
10.15 A.Bru'
10.40 Break
11.00 F.Sepulcre
11.25 G.Pescarmona
11.50 G.Bianciardi
12.15 P.Waliszewski

1 - 3 pm: LUNCH

3.0 pm: SESSION 4: Chairman: G.Landini

3.00 J.P.Rigaut
3.45 G.De Vico
4.10 A.Piantanelli
4.35 H.Libouban
5.0 E.Oczeretko
5.25 A.Kyrylyuk

8 pm: DINNER

Friday 10

9.30 am: SESSION 5: Chairman : A.Kyrylyuk

9.30 B.Nielsen
9.55 B.Weyn
10.20 F.Marinelli
10.45 G.Losa
11.05 Break
11.25 N.Dioguardi
11.50 H.Hahn
12.15 H.Schwarzenbach
12.40 S.Montagnese

1-3 pm: LUNCH

2.30-3.30 pm: POSTER SESSION


Public lecture by Prof. B.Mandelbrot


8.30 pm - ?: FRACTAL DINNER and MUSIC

Saturday 11

9.30 am: SESSION 6: Chairman: N.Dioguardi

9.30 T.Mattfeldt
10.15 M.Buiatti
10.45 H.Chouard
11.10 B.Meyer
11.35 D.Cosandey
12.0 G.Damiani
12.20 L.Nottale


1.15 pm: Survival's LUNCH


The sequence of the speakers within a single session may be modified by decision of the chairman.

The allotted time for each speech is inclusive of five minutes discussion.

The titles of all presentations are listed in the section Updates and News.


Abstracts submission

Abstracts of one or two pages (A4) should be submitted to the Scientific Committee by e-mail as attached document (Format: Word, rtf, text) until February 20, 2000. They will be reproduced as submitted.

Attendance: is limited to 80-100 participants

Information on your participation to the Symposium and indication of the topic of your paper: January 31, 2000
Deadline for submission of abstracts: February 20, 2000.
Notification of acceptance February 27, 2000

Scientific and Organizing Committee

Prof. Dr.Gabriele A. Losa, chairman
Laboratorio di Patologia Cellulare, Institute of Pathology,CH-6601 Locarno
Faculty of Sciences, University of Lausanne, 1000 Lausanne, Switzerland
phone: +41-91-7562680; fax +41-91-7562691;

Prof.Dr.Theo F.Nonnenmacher, co-chairman
Abteilung für Mathematische Physik,
University Ulm, 89069-Ulm , Germany
phone: +49-731-5022990; fax: 731-5023003; e-mail:

Prof. Dr. Danilo Merlini
Centro di Ricerca in Fisica e Matematica,
v.F.Rusca 1, 6600 Locarno, Switzerland
phone:+41-91-7516424; fax:+41-91-7516425; e-mail:

Prof. Dr. Em.Ewald R.Weibel.
Maurice E.Mueller Foundation, University Bern
3000 Bern, Switzerland
phone: +41-31-3820031: fax: +41-31-3823087; e-mail:

Registration Fees

SFr. 120.- .The registration fee covers the access to the symposium, social events and a copy of the abstract booklet.

Hotel registration

In Hotel Centro Seminariale Monte Verità
  • single room + breakfeast: sfr. 110.- / night
  • double room + breakfeast: sfr. 77.- / night
  • Alternative Hotel (walking distance)

    Accomodation will be organized by the Direction of Centro Seminariale, Monte Verità, Ascona Fax: +41-91-780-51 35; Telephone: +41-91-791 01 81; e-mail: reception@csf-mv.ti-edu
    More infomations about Hotels :

  • Travel Informations

    Centro Seminariale Monte Verità, CH-6612 Ascona, Ti, Switzerland. Website: http://www.csf-mv.ethz

    Locarno Station-Ascona terminal: bus no. 31

    From Ascona to Centro Seminariale Monte Verità,minibus servive (BUXI) by Ascona Taxi, phone: 0041-91-7917777. Location:Underground Parking, via Baraggie, walking distance from Bus Terminal.

    Social events

    FRIDAY 10 March: 6 pm

    Celebration of Benoit Mandelbrot's 75 th Birthday

    Public Conference by Prof. Benoit Mandelbrot


    Salone Palazzo SOPRACENERINA

    Piazza Grande, Locarno

    FRIDAY 10, 8.30 pm: Fractal Dinner with musical entertainement at the Restaurant in Monte Verità.

    SATURDAY 11, afternoon: visit (for interested people) to the new Academy of Architecture at the University of the Italian Switzerland, Mendrisio. Meeting with Prof.s Mario Botta and Aurelio Galfetti, architects.

    Miscellaneous Informations

    T.F.Nonnenmacher, G.A.Losa, E.R.Weibel.
    Fractals in Biology and Medicine, vol I,1994
    Birkhäuser Verlag P.O.Box 133, CH-4010 Basel / Switzerland
    website: http://www.birkhä

    G.A.Losa,T.F.Nonnenmacher, D.Merlini, E.R.Weibel.
    Fractals in Biology and Medicine, vol II, 1998
    Birkhäuser Verlag P.O.Box 133, CH-4010 Basel / Switzerland

    Useful links:
    European Society for Analytical Cellular Pathology :
    Swiss Society for Optics and Microscopy :
    Swiss Society of Cell Biology, Molecular Biology and Genetics:
    Italian Society of Chaos and Complexity (SICC:
    Center for Research in Physics and Mathematics (CERFIM:
    Italian Society for Electron Microscopy (SIME:
    Chaos at Maryland:
    Society for Mathematical Biology:
    Microscopy Society of America:
    Swiss Academy of Sciences SAS:

    News and Updates

    Abstracts must not exceed two pages(format A4)including references 
    and figures and be submitted to the organizers by e-mail. Submitted abstracts 
    will be published in a regular issue of Biology Forum, an international 
    multidisciplinary Journal.
      March 3, 2000
    - B.Sapoval, M.Filoche, *E.R.Weibel. 
      Laboratoire de Physique de la Matière Condensée, C.N.R.S. 
      Ecole Polytechnique, 91128 Palaiseau, France; Centre de Mathématiques
      et de leurs Applications, Ecole Nornale Supérieure de Cachan, 
      94140 Cachan, France.
      *Department of Anatomy,University of Berne,CH-3000 Bern, Switzerland.
      Acinus morphology and optimal design of mammalian lungs.
    - Gabriel Landini.
      Oral Pathology Unit, School of Dentistry, The University of Birmingham,
      St.Chad's Quensway, Birmingham B4 6NN, England.
      Fractals in organogenesis and carcinogenesis: algorithmic pattern formation?
    - Laurent Nottale. 
      DEAC. UMR 8631 CNRS. Observatoire de Paris-Meudon. 
      F-92195 Meudon Cedex, France.
      On the possible fractal structure of the evolutionary tree.
    - G.P.Pescarmona,*M.Scalerandi, B.Capogrosso,*P.P.Delsanto.
      Dip.Genetica, Biologia e Biochimica,Via Santena 5bis, Università di Torino,
      Torino e *INFM, Dipartimento di Fisica,Politecnico di Torino,10126 Torino.
      A simulation of cancer growth and metastasis based on the limitation 
      of essential nutrients. 
    - *P.P.Delsanto,V.Agostini,*B.Capogrosso,*M. Scalerandi,G.B.Pescarmona.  
      Dip.Genetica, Biologia e Biochimica,Via Santena 5bis, Università di Torino,
      Torino e *INFM, Dipartimento di Fisica,Politecnico di Torino,10126 Torino.
      Non-classical,non-linear effects in physics,geophysics and biology.
    - *E.Castelli, G.L.Panatton, *T.Todros.
      Dipartimento di Anatomia, Farmacologia e Medicina Legale, Università 
      di Torino, e *Dipartimento di Discipline Ginecologiche e Ostetriche,
      Università di Torino,Torino,Italy.
      Ultrasonographic nuchal translucency and development of the lymphatic 
      system in the fetus: can they be explained by a fractal model?.
    - V.Péan,M.Quayoun,C.Fugain,B.Meyer,C.H.Chouard. 
      ENT Research Laboratory,CHU  St-Antoine, 184 rue du Fbg St-Antoine.
      F-75012 Paris, France.
      Fractal approaches of pathological voices.
    - M. Quayoun, V. Péan, B. Meyer, C.H.Chouard.
      ENT Research Laboratory, CHU St-Antoine, 184 rue du Fbg St-Antoine.
      F-75012 Paris, France.
      A fractal approach of speech vowels.
    - David A. Cosandey. Credit Suisse. CH-8000 Zurich, Switzerland
      The fractal dimension of the coastline as a determinant of western 
      leadership in science and technology.
    - Gionata De Vico, G. Piedimonte, B. Macrì. 
      Dipartimento di Patologia, Malattie infettive e Parassitarie 
      ed Ispezione degli Alimenti di O.A. Sezione di Patologia Generale 
      e Anatomia Patologica Veterinaria, Facoltà di Medicina Veterinaria,
      Università di Messina, Via S.cecilia 30, 98123 Messina, Italy.
      The fractal dimension of the inner surface of neoplastic mammary ducts 
      in mammary fibroadenomas and mammary adenocarcinomas of dog and cat.
    - Francesc Sepulcre Sànchez. 
      Dep. Enginyeria Química,Universitat Politècnica de Catalunya,
      Comte d'Urgell 187, 08036 Barcelona, Spain.
      Recognition of malignant mesothelioma cells.
    - Antonio Brú. 
      C.I.E.M.A.T, Avenida Complutense,22, 28040 Madrid, Spain.
      Universal scaling of tumor growth.
    - Andrei P. Kyrylyuk. 
      Solid State Theory Department, Institute of Metal Physics,
      of the National Academy of Sciences of Ukraine, 
      prospect Vernadskogo 36,
      Kiev-30, Ukraine 01030.
      The universal dynamic complexity,extended dynamical fractal 
      and its application to living systems.
    - Michael Meyer,O.Stiedl, J.Spiess. 
      Department of Physiology, Max Plank Institute for Experimental 
      Medicine, Hermann Rein Str.3, D-37075 Goettingen, Germany.
      Fractal scaling of heart rate dynamics in man and mice
      (normal and transgenic).
    - B.Kerman,Michael Meyer.
      Department of Physiology, Max Plank Institute for Experimental 
      Medicine, Hermann Rein Str.3, D-37075 Goettingen, Germany.
      Multi-fractal states of cardiac rhythm.
    - Jean Paul Rigaut, Vénus Sharifi-Salamatian. 
      IUH,IFR,Hôpital St.Louis, 1 avenue Claude Vellefaux,
      75475 Paris, France.
      Heterogeneity: from asymptotic fractals to geostatistics.
    - Bruce J. West. 
      FAPS, Army Research Office, Research Triangle, nc 27709-22111,U.S.A.
      Fractional calculus and memory in biomedical time series.
    - Marcello Buiatti, Claudia Acquisti,Giuseppe Mersi,
      Patrizia Bogani, Marco Buiatti.
      Dipartimento di Biologia Animale e Genetica. Università di Firenze. 
      Firenze, Italy
      The biological meaning of DNA correlations.
    - H.Libouban,M.F.Moreau,E.Legrand,M.F.Baslé,M.Audran,D.Chappard. 
      LHEA: Lab.Histologie Embryologie,Faculty of Medicine,University
      and CHU of Angers, 49033 Angers, France.
      Histomorphometric descriptors of bone architecture (fractal dimension 
      and connectivity indeces) are better predictors of bone loss than mineral 
      density (DXA)in the orchidectomized rat.
    - D.Chappard,A.Chennebault,M.F.Moreau,E.Legrand,M.Audran,M.F.Baslé. 
      LHEA: Lab.Histologie Embryologie,Faculty of Medicine, University 
      and CHU of Angers, 49033 Angers, France.
      Texture analysis of X-ray micrographs by fractal geometry are better 
      predictors of bone loss than mineral density (DXA) in a rat model of 
      localized disuse osteopenia.
    - E.Oczeretko. 
      Institute of Physics, University of Bialystok, 15-424 Bialystok, Poland.
      Fractal dimension: a new diagnostic parameter in medicine?
    - Hiroko Kitaoka.
      Div. of Functional Diagnostic Imaging, Osaka University Medical School,
      Osaka, Japan.
      1.Three-dimensional model of the human airway tree based on a fractal 
      branching algorithm.
      2.Three-dimensional model of the human pulmonary acinus based on a 
      space-filling labyrinthe algorithm.
    - Jerzy Konarski.
      Faculty of Chemistry, A.Mickiewicz University, Grunwaldzk 6, 
      60-780 Poznam, Poland.
      Stable and unstable rovibrational states-route to chaos.
    - B.Nielsen,F.Albregtsen,H.E.Danielsen.
      Department of Informatics, University of Oslo, P.O.Box 1080 Blindern,
      N-0136 Oslo, Norway.Division of Digital Pathology,
      The Norvegian Radium Hospital, Montebello, N-0310 Oslo, Norway.
      Using fractal signature and lacunarity distance matrices to extract 
      new adaptive texture freatures from cell nuclei.
    - *C.Castelli,**T.F.Nonnenmacher,*°G.A.Losa.
      *Laboratorio di Patologia Cellulare, Istituto di Patologia, 6600 Locarno, 
      °Istituto di Studi Scientifici Interdisciplinari, 66oo Locarno, Switzerland 
      ** Abteilung für Mathematische Physyk, Universität Ulm, Ulm, Germany.
      Morphofractal reorganization of plasma membrane and nuclear components 
      during the apoptotic process of breast cancer cells. 
    - Giuseppe Damiani.
      IDVGA-CNR, via F.lli Cervi 93, 20090 Segrate (MI), Italy.
      Power laws, metabolism and evolution.
    - Fahima Nekka.
      Faculté de Pharmacie, C.P. 6128, Montréal H3C 3J7, Canada
      Lacunarity analysis.
    - Przemko Waliszewski.
      Department of Theoretical Chemistry, University of Poznan,
      Grunwaldzka 6, 60-780 Poznan, Poland.
      A relationship between time and space in cellular system 
      with fractal structure.
    - Horst K.Hahn, Carl J.G.Evertsz, Hans-Otto Peigen.
      MeVis, Universität Bremen, 28359, Bremen, Germany.
      Fractal properties, segment anatomy and interdependence 
      of the human portal vein and the hepatic vein in 3D.
    - Gerd Baumann(1),Siglinde Kleinschmidt(2),Albrecht K.Kleinschmidt(2).
      (1)Department of Mathematical Physics, University of Ulm, 
      (2) University of Ulm Albert-Einstein-Allee 11,D-89069 Ulm,Germany.
       A headful of T4 Coliphage DNA: dynamical Modelling.
    - Torsten Mattfeld °,Hans-Werner Gottfried +,Hans A.Kestler ".
      Institute of Pathology°, Department of Urology +, 
      Department of Neural Information Processing ",
      University of Ulm, Oberer Eselsberg M23, 
      D-89081 Germany.
      Classification of prostatic cancer using artificial neural networks.
    - Nicola Dioguardi, Fabio Grizzi.
      Istituto Clinico Humanitas, Via Manzoni 56,20089 Rozzano(Mi),Italy.
      Fractal dimension exponent for quantitative evaluation 
      of liver collagen in bioptic specimens.
    - H.R.Schwarzenbach,M.Essig,J.Prim,J.Tuma, L.Braun.
      Swiss Ultrasound Society (SGUM),6815 Melide,Switzerland.
      Fractal analysis of signal-intensity-variance in liver 
    - B.Weyn °*, W.Jacob*, A.Van Daele*, D.Thompson°, H.Bartels°, P.Bartels°.
      °Optical Sciences Center, University of Arizona, Tucson, AZ,USA 
      *Centre for Electron Microscopy, University of Antwerp(UIA),
      Universiteitsplein 1, B-2610 Antwerpen, Belgium.
      Quantification of nuclear signatures based on geometrical 
      and fractal features.
    - Norbert Südland,Christine Volz,Theo F.Nonnenmacher.
      Abteilung für Mathematische Physik, Universität Ulm, 
      Albert-Einstein-Allee 11,D-89069 Ulm, Germany
      A fractional Calculus approach to adsorbate dynamics 
      in nanoporous materials.
    - Nicoletta Sala.
      Academy of Architecture, University of Italian Switzerland,
      6853 Mendrisio, Switzerland.
      Fractals in architecture: some examples. 
    - D.Pascoli*,S.Montagnese°,T.Minelli*,A.Pesavento",
      PG. Marchetti°,P.Amodio°.
      *Dept.of Physics and °Dept.of Clinical and Experimental 
      Medicine,University of Padova,"I Psychiatry,
      General Hospital of Padova, Padova, Italy.
      The EEG signal in hepatic encephalopathy:from time-domain 
      analysis towards fractional brownian Processes.
    - Carlos Felgueiras
      INEB-Instituto de Engenharia Biomédica
      Praça do Coronel Pacheco,1, 4050 Porto, Portugal.
      Fractal Modeling of film growth on bioactive surface.
    - Jürgen.W.Dollinger, Theo.F.Nonnenmacher.
      Department of Mathematical Physics, University of Ulm
      Albert-Eistein-Allee 11, D-89069 Ulm/Donau, Germany
      Bi-asymptotic fractals; Lower and upper bounds.
    - A.Piantanelli*,S.Serresi*,A.Giacchetti*,G.Libertini*,
      *Unit of Dermatology-Geriatric Hospital and 
      °Centre of Biochemistry-Gerontologic Research Department; 
      Estimation of image contour fractal dimension of human 
      pigmented skin lesions.
    - Fiorenzo Marinelli.
      Istituto di Citomorfologia C.N.R., Via di Barbiano 1/10, 
      40136 Bologna, Italy
      Fractal analysis of cromatin during apoptosis.
    - G.Bianciardi,L.Leoncini,S.Lazzi,A.V.Lalinga, P.Luzi.
      Istituto di Anatomia e Istologia Patologica, 
      Università di Siena, Via delle Scotte 6,53100 Siena, Italy
      Fractal analysis of the bone marrow in refractory anemia 
      and acute leukemia.
    - D.Merlini°,L.Rusconi°,A.Bernasconi*
      °Center for Research in Physics and Mathematics (CERFIM /ISSI),
      v.Rusca 1, 6600 Locarno, Switzerland 
      *Swiss Center for Scientific Computing (CSCS),6928 Manno,Switzerland
      Chaos and complexity from the Riemann Hypothesis
    - Sergio Albeverio.
      Institute for Mathematics and Probability,
      University of Bonn, Bonn,Germany
      Branching processes and biological models.


    The Symposium will be held under the patronage of the International Society of Stereology, International Society for Diagnostic Quantitative Pathology, European Society for Analytical Cellular Pathology, Swiss National Science Foundation, Swiss Academy of Sciences, Maurice E.Müller Foundation, Swiss Society of Cytometry, Swiss Society of Cell Biology, Swiss Society of Microscopy, Dipartimento Istruzione e Cultura (Ufficio Studi Universitari) and Dipartimento Opere Sociali of the Republic of Ticino, Accademia di Architettura of the University of Italian Switzerland (USI), Swiss Center for Scientific Computing, Manno, Società Ticinese di Scienze Naturali, Lugano; Institute for Scientific Interdisciplinary Study, Locarno; Research Center for Mathematics and Physics, Locarno (Switzerland).


    Public Institutions

    Dipartimento Istruzione e Cultura /Ufficio Studi Universitari e
    Dipartimento Opere Sociali, Repubblica e Stato del Canton Ticino, Bellinzona
    Swiss National Science Foundation, Berne
    Swiss Academy of Sciences, Berne
    Major and City of Locarno

    Private Institutions

    Banca dello Stato del Canton Ticino, Bellinzona
    Maurice E.Müller Foundation, Berne
    Banca del Gottardo, Lugano
    Banca della Svizzera Italiana, Lugano
    Banco di Lugano, Lugano
    Pharma Consulting Marion Senn GMBH, Burgdorf
    Becton Dickinson BD, Basel

    The Fractal Dimension of the Coastline as a Determinant of Western Leadership in Science and Technology

    David Cosandey
    Independent scholar, 8700 Kusnacht ZH, Switzerland, e-mail:

    Summary: This paper argues that the fractal dimension of the Western European coastline was an important causal factor behind the continent's tremendous success in science and technology over the last centuries. The nicely articulated coastline fostered the political and economic developments necessary for science to flourish. These political and economic conditions of scientific progress are briefly outlined here. The fractal dimension is used as a means to precisely quantify the coastline's degree of articulation. Measurements are made in the 100 to 1,000 km range. Western Europe's coastline is shown to have a significantly higher fractal dimension than those of the Middle East, India and China.

    1 Introduction

    Why did Western Europe succeed scientifically the way it did during the last centuries? And why didn't other civilizations? Why was modern science and the industrial revolution invented by the West? I shall argue in this paper that the causality chain leading to the European scientific "miracle" started with the high fractal dimension of the Western European coastline.
        The Western part of the European continent is the only densely populated area on Earth boasting as many peninsulas, gulfs, straits, inland seas, while still being for the most part an interconnected land.
        Such an articulated coastline enhances trade, because sea accessibility makes maritime transportation easier. The sea route is much better than river or land transportation. It is tremendously cheaper, it is less limited in capacity and enjoys more freedom. Before modern times, it was even faster. Thus a high level of coastline articulation, by bringing the sea closer to all places, allowed the economy to thrive in the long-term.
        An articulated coastline defines naturally limited core areas (peninsulas, half-peninsulas, islands) within which polities can live their lives without being too much disturbed, as the sea is the best possible boundary for a state. Britain, Spain, France, Denmark, Sweden are such ancient states, well delimited by the sea. The shape of the Western European coastline helped the continent to remain divided between stable and long-lasting states.
        Thus the Western European coastline shape most probably enhanced economic growth and fostered the continent's stable states system. We shall argue that this political and economic background was the necessary and sufficient condition for the flourishing of science.

    2 A Political and Economic Theory of Scientific Progress

    A rich economy allows scientific and technical progresses in many ways: It generates a surplus, necessary for science and the arts to thrive. Moreover, merchants, bankers and entrepreneurs are obsessively looking for accuracy, counting, number-using. When successful, they gradually impose their science-friendly mentality upon society. Even better: merchants, bankers and entrepreneurs have a vested interest in science and technology: they support developments in mathematics (accounting arithmetic, higher-degree equations for interest rate calculations, statistics for stock exchange trading and insurances, etc.). In the Middle Ages, they supported the development of clocks for measuring manufacturing and travelling times, of accurate maps for travelling, of astronomy for navigation, and of course of all sorts of technical devices, since increasing manufacturing productivity and decreasing transport costs brings profit.
        Stable political division helps science and technology in many ways. It generates freedom. No center has a monopoly of power, no government can control everything. The diversity of legislations grants a much larger overall liberty to science. Suppressed in a given country, a scientist or a technician can look for shelter in another one (these effects were already identified by various authors, like [1] and [2]). But there is more. Competition between states generates a profitable stimulation. Every government wants to do better (or at least not worse) than neighboring countries. Hence governmental support for science academies. War exercises a continuous pressure towards modernization, it creates a strong government interest for new technical devices and for improving technical knowledge and education. But unfettered war wreaks havoc, thus the need for stable political division.
        The same holds true for the smart European scientific professional structure: universities, royal academies, private schools of mathematics. The institutions that allowed scientists to make a living while doing research could come to life only thanks to the good economic and political situation of Western Europe. When studying their history, it is easy to verify that these institutions thrived because of the possibility to flee to a another state, the availability of financial means, inter-state prestige and military rivalry.
        Hence, we may formulate a general rule: in a given region (we should look at a complete region – a region mainly isolated from major outside influences –, i.e. a civilization earlier, and the world nowadays), science and technology can advance if and only if the region hosts a rich and stable states system. Western Europe enjoyed a growing trade and manufacturing, and was divided between long-lasting competitive kingdoms during the whole 2nd millennium; this is why it succeeded the way it did. Other civilizations did not form rich and stable states system during as long a period as Europe, that is why, on the whole, they had less success in science.

    3 Eastern Europe and Other Civilizations

    The rich states system theory explains quite well the different stages of the scientific evolutions of Western Europe, Eastern Europe, the Middle East, India and China. As I showed in Le secret de l'Occident [3], each time prosperity and stable division are there, science flourishes. Conversely, when other conditions are rife, like political unity, fast-changing boundaries, civil wars and/or economic doldrums, science recedes.
        In particular, that theory sheds light upon the mysterious drop of Chinese scientific development around 1300: at this time, China departed from a "stable states system" state towards political unity. China did not enjoy favorable conditions again during centuries. It first entered unity, then suffered a civil war, then fell into unity agarn.
        The difference between Western and Eastern Europe is neatly solved as well.
        The steadily weak performance of Eastern Europe in science and technology can be linked to the bad economic and political conditions which it suffered along the 2nd millenium. Eastern European states were unstable, they underwent fast boundary moves, they appeared and disappeared. Trade was weak, manufacturing rickety.
        Merchants never thrived half as well as their Western equivalents. This can be linked to the fact that Eastern Europe does not enjoy as good a shore profile as Western Europe: it is a mainly landlocked area. Vast surfaces are deprived of sea access: the seas are too far away – and are often closed or ice-blocked. The vast land compactness explains why the economy remained sluggish (sea trade could not play a role) and why the region's states were brittle and short-lived (no natural boundary protected them).

    4 Measuring Fractal Dimensions of Coastlines

    4.1 Indices to assess a Coastline

    The quality of a coastline (its degree of indentation) can be quantified with various indices, which we shall briefly compare here.
        A very simple procedure is to measure the distance to the sea of the farthest point inland. This measurement, a first indication at best, gives the best note to Western Europe (see table).
        Another, more elaborate, method consists in measuring the coast length and dividing it by the surface of enclosed land. This is the so-called "coastline development index". We display in the table below the results obtained by using shoreline measurements from Lucchini & Voelckel [4]. The development index sets Western Europe far above, at first rank.
        The development index, however, is not a completely satisfying quantity because the length of the coastline is no definite quantity. A coastline actually is a fractal object, with no upper bound on its length. Comparison between development indices makes sense, to a limited extent, only so far as the coast lengths were measured at identical scales. The degree of articulation of the coastline is best measured by the fractal dimension.

    4.2 Methodology

    To measure coastlines fractal dimensions, we relied on the Richardson technique (see e.g. [5]), which originally inspired B. Mandelbrot in its exploratory work on fractals.
        The length of the coastlines of Europe, the Middle East, India and China were measured on the map with a compass of an aperture of 1,000 km. The compass approximated the shoreline with a broken line, whose length could be easily measured. The same operation was repeated with smaller and smaller segments. The segments varied between 1,000 km and 100 km.
        The lengths of the broken lines were plotted versus segment lengths in a logarithmic-scale graph. The slope of the curve was taken as the fractal dimension. It was thus an "intermediary" fractal dimension, i.e. taken within a given segment range, and not the fractal dimension according to the mathematical definition, where one should look for the limit when segments shrink to zero, i.e. at the slope of the logarithmic curve in the graph at infinity.
        The justification is the following: first, in a natural object like a coast, there is no guarantee that the slope of the logarithmic curve will converge to a defined limit.
        Second, when looking for factors impacting long-term history, we judge the 100-1000 km range much more relevant than, say, the millimeter or micrometer ranges.
        For each civilization, a start point and an end point were defined for the measurements on the map. The length of the broken line was defined as the number of entire steps plus the remaining length up to the end point.
        The broken line follows the continental coastline. Islands receive separate broken lines as soon as they are large enough for the segment to "see" them. In such cases, a start and an end points have to be chosen for the island, introducing some arbitrariness in the process. To reduce this arbitrariness, we aimed at maximizing the measured length at each segment scale. Island coastline lengths were added to the continental length.
        Sometimes, the segment has the choice between two intersections on the map.
        For example, at the "heel" of Italy, the 316 km segment sees both the Italian Adriatic coast and the Greek coast. In such cases, preference was given to the closest point along the coast, i.e. the one maximizing the final measured length.
        An alternative calculating method to assess fractal dimensions would be to include terrestrial domain borders. These non-maritime border lines would be considered non-fractal, bringing a constant kilometer add-on on each shore length measurement. This approach would better mirror the impact of large terrestrial areas with little access to the sea, like Central Asia, which are not "seen" with a compass sticking to maritime borders. It would lower the final fractal dimension of terrestrial areas, yet increasing the Western European advantage.

    4.3 Conventions

    Be it for deriving fractal dimension, maximum distance to sea, or coastline development, the four regions to be compared (Europe, Middle East, India, China) were defined as follows:
        "Western Europe" includes all territory west of the line Lubeck-Venice, with the Swedish-Norwegian peninsula added. "Western & Central Europe" contains all of European territory except the pre-1990 Soviet Union and Finland.
        "The Middle East" was defined as Africa north of the Sahara, Arabia, Mesopotamia, Iran and Central Asia. The Southern limit was the Sahara desert around present-day boundaries of Morocco, Algeria, Lybia and Egypt. The Northern limit was the Caucasus and Anatolia. Central Asia has only terrestrial limits. The starting point of the first coastline was in Southern Morocco, ending at the present-day Syrian-Turkish border. The second coastline was that of the southern Caspian sea. The third coastline started on the Sudanese coast and ended at the starting point of India.
        "India" was defined as the whole Indian subcontinent. That includes present-day Pakistan, Republic of India, Bangladesh, Nepal, Bhutan, Sri Lanka, Maledives, Laccadives. The start point was near present-day border between Pakistan and Iran, on the west of the Indus delta. The end point was on the Eastern side of the Gange delta, within present-day Bangladesh.
        "China" was defined as the area populated by Han until around 1700. This includes the present People's republic of China without Manchuria, Inner Mongolia, Eastern Turkestan and Tibet. The coastline extended from Tianjin (harbor of Peking) down to the present Vietnamese border. Taiwan and Hainan were included.
        The length of the coastlines was successively measured using 1,000 km, 316 km, and 100 km segments, so that the corresponding points were equally spaced in the logarithmic space. More segments can anyway be added inbetween if wished. A graph was built plotting increasing coastline length versus decreasing segment length. A best fit for the slope was obtained. This slope was dubbed the "intermediary fractal dimension" in the range 100-1,000 km.

    5 Results and Conclusions

    The results of different coastline measurements are displayed in the table below.

    Max. distance to the sea (km) Development indice (10^-5 km/km2) "Intermediary" fractal dimension
    Western Europe
    Western & Central Europe
    Middle East

    Table: quantifying the articulation/ indentation of the coastline

    The results clearly show that Western Europe has a much higher fractal dimension (1.47) than China (1.26), India (1.19) and the Middle East (1.12). These differences are significant because these figures can take values between 1 and 2, theoretically. Practically, they vary in an even narrower range. Indeed, a coastline with a fractal dimension as high as, say 1.8 or 1.9, is barely thinkable.
        Thus, what is seen with the eye is confirmed by quantitative measurements. Western Europe boasts a much more articulated coastline than other civilizations. It has several large peninsulas (Spain, Italy, Denmark, Sweden-Norway), several islands more than 100 km wide (Britain, Ireland, Iceland, Sicily, Sardinia, Corsica, Sjaelland, Gotland). Whereas the Middle East just has nascent peninsulas (Tunis, Byrte) and no large island. India has only one peninsula (Gujarat) and one large island (Ceylon). China has only one peninsula (Shandong) and two islands (Taiwan, Hainan).
        The intermediary fractal dimension tell the same story as the other indices tested. Western Europe has a much more indented coastline than other civilizations. This geographical factor, through a complex chain of political and economic causalities, might have given Western Europe its edge in science and technology during the second millenium. Hence, although surprising at first sight, the European scientific "miracle" seems to be, indirectly, a present from geology.

    [1] Braudel F., Civilisation matérielle, économie et capitalisme (XVe-XVIIIe siècle), Armand Colin, Paris (1979).
    [2] Jones E., The European Miracle. Environments, Economies and Geopolitics in the History of Europe and Asia, Cambridge University Press, Cambridge (1980).
    [3] Cosandey D., Le Secret de l'Occident, Arléa, Paris (1997).
    [4] Lucchini L., Voelckel M., "Les Etats et la mer, le nationalisme maritime", in: La Documentation française (1977), quoting figures from Geographic Bulletin no3, Oct 1969.
    [5] Gerald E., Classics on Fractals, Addislon-Weslex, Reading, Massachussetts, Etats-Unis (1993).

    Created: 05 Dec 2000 – Last modified: 19 Feb 2017