ISC 5451: Fractals and Chaos For the Life Sciences

An Introduction Illustrated With Biomedical Applications

mathematical level: calculus and differential equations

Fractals and Chaos have attracted wide attention and excitement in mathematics
and the physical sciences. These ideas are now being used to achieve a better
understanding of DNA, proteins, ion channels, nerve cells, muscle cells, blood
vessels, the heart, the lungs, and the brain. This course will explain the
properties of Fractals and Chaos and illustrate them with biomedical

Instructor: Dr. Larry S. Liebovitch
Center for Complex Systems and Brain Sciences
Center for Molecular Biology and Biotechnology
Department of Psychology
Department of Biomedical Science


Florida Atlantic University
Fleming Hall, Room 317, Boca Raton
Tuesday, Thursday: 11:00 AM - 12:20 PM

        Fractal Physiology
        by J. B. Bassingthwaighte, L. S. Liebovitch, B. J. West
        Oxford University Press, 1994

        by Jens Feder
        Plenum Press, 1988

        Chaotic and Fractal Dynamics
        by Francis C. Moon
        John Wiley & Sons 1992
        (or the 1987 first edition called Chaotic Vibrations)

        Chaos: Making a New Science
        by James Gleick
        Viking Press 1987

        Fractals and Chaos: Simplified for the Life Sciences
        by L. S. Liebovitch
        Oxford University Press, 1998

BLW = pages in Bassingthwaighte, Liebovitch, and West
F   = pages in Feder
M87 = pages in Moon (1987 first edition)
M92 = pages in Moon (1992 second edition)
G   = pages in Gleick


1.      Introduction and Overview of fractals
                (BLW:v-viii,3-7, G:81-118)
2.      Dimension
                (BLW:11-44, F:11-18, M87:205-218, M92:325-338)
3.      Self-similarity and scaling
                (BLW:11-21, F:26-30,184-188)
4.      Biological examples of self-similarity and scaling
                (BLW:45-62,214-225, F:229-243)
5.      Statistical properties
6.      Biological examples of statistical properties
                (BLW: 210-214,225-228,236-262)
7.      Rescaled range analysis and random walks
                (BLW:63-107, F:149-162,163-183)
8.      Cell membranes and ion transport
                (BLW: 177-184,202-203)
9.      Using fractals to determine the physical properties of ion
        channel proteins
                (BLW: 184-209)

10.     Overview of chaos
                (BLW: 136-146, G:1-80)
11.     Phase space and bifurcations
                (G:119-153, M87:1-36,191-204,218-22, M92:1-46,127-132,338-341)
12.     Logistic and Lorenz
                (M87:56-65,166-172, M92:32-35,68-82,115-142)
13.     Biological examples of bifurcations and chaos
                (BLW: 300-305,317-320, M87:84-119, M92:147-211,212-214)
14.     Experimental measures of chaos
                (BLW: 147-173, M87:37-56,127-153,222-242,
15.     Biological examples of chaos
                (BLW: 305-317,320-327)

Course Policies

  1. Attendance: Students are expected to attend all scheduled classes. If you miss a class you are responsible for ALL the material covered during that class, including lecture material and rules and regulations about the course (such as these rules).
  2. Withdraw: It is the responsibility of the student to withdraw from this class, should that status be desired - the instructor cannot withdraw students from the course. The instructor will not give the grade of "I" in lieu of a grade of "D" or "F". The grade of "I" will be considered only in exception cases (such as serious illness) for students who are presently performing at a C or higher level in the course.
  3. Homework Problems: All homework problems must be turned in on the dates assigned. Late homework problems will be accepted up to 1 week late, but they will be penalized. No homework problems will be accepted over 1 week late. You will have the option of redoing each homework assignment to improve your grade on it, BUT if it was not turned in on the date assigned, it will still be penalized. Just to repeat, ANY homework first turned in later than 1 week will count as zero. Homework problems must be submitted on 8.5 x 11 inch paper or A4 paper if you are a very sophisticated world traveller. Handwritten homework that is not readable is not acceptable. They should have a cover sheet with your full name. You are requested to make a copy of all material turned in for credit to guard against loss or damage.
  4. Grade: The grade will be entirely based on the homework assignments and a final exam. Assignments not turned in will count as zero.

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