Uploaded March 2023 | Updated September 2026, 2 weeks ago
This video shows the calculation of the logistic equation in MSX BASIC. The code of the program is shown at the beginning of the video.
The logistic equation was developed to model the growth of populations. It can be written as S(i+1) = r·S(i)·(1-S(i)), where S(i) is the size of the population on a particular generation i (normalized as a fraction of 1 with respect to a maximum possible population, S = Population/Maximum population), S(i+1) is the size of the population on the next generation i+1, and r is a constant model parameter.
The program graphically shows the evolution of the size of the population. The generations advance over the horizontal axis, while the size of the population is represented on the vertical axis. If sound is enabled, the sound is also proportional to the size of the population (with higher notes corresponding to bigger populations). The program calculates this evolution for several values of the parameter r, ranging from 0 to 4. Every time the screen clears, the program begins the calculation with a new, higher value of r.
The program shows the variations in the dynamic behavior of the equation as r increases, starting with an initial population of size S = 0.1. With low values of r, the population becomes extinct as S falls to 0. With higher values, the population stabilizes in a non-zero size. Even higher values produce more peculiar behaviors: first an oscillatory evolution over a periodic orbit of period 2, then a periodic orbit of period 4, and finally very complex patterns as r approaches 4. The astonishingly complex behavior of this apparently very simple equation makes it one of the favorite case studies of non-linear dynamics and chaos theories.
This video shows the calculation of the logistic equation in MSX BASIC. The code of the program is shown at the beginning of the video.
The logistic equation was developed to model the growth of populations. It can be written as S(i+1) = r·S(i)·(1-S(i)), where S(i) is the size of the population on a particular generation i (normalized as a fraction of 1 with respect to a maximum possible population, S = Population/Maximum population), S(i+1) is the size of the population on the next generation i+1, and r is a constant model parameter.
The program graphically shows the evolution of the size of the population. The generations advance over the horizontal axis, while the size of the population is represented on the vertical axis. If sound is enabled, the sound is also proportional to the size of the population (with higher notes corresponding to bigger populations). The program calculates this evolution for several values of the parameter r, ranging from 0 to 4. Every time the screen clears, the program begins the calculation with a new, higher value of r.
The program shows the variations in the dynamic behavior of the equation as r increases, starting with an initial population of size S = 0.1. With low values of r, the population becomes extinct as S falls to 0. With higher values, the population stabilizes in a non-zero size. Even higher values produce more peculiar behaviors: first an oscillatory evolution over a periodic orbit of period 2, then a periodic orbit of period 4, and finally very complex patterns as r approaches 4. The astonishingly complex behavior of this apparently very simple equation makes it one of the favorite case studies of non-linear dynamics and chaos theories.
