Realistic Predator Prey Model
dN / dt = N * [r * (1 – N / K) – k * P / (N + D)] (Prey Equation)
dP/ dt = P * [s * (1 – h * P / N)] (Predator Equation)
To reduce the six-parameter model to a more manageable three parameter one introduce the following variables and parameters
u(w) = N(t) / K
v(w) = h * P(t) / K
w = r * t
a = k / (h * r)
b = s / r
d = D / K
du / dw = u – (1 – u) – a * u * v / (u + d)
dv / dw = b * v * (1 – v / u)
In my program a = alpha, d = beta, and b = gamma
All the images were generated using the complex polynomial as shown below:
z1 = z0 ^ n + c0
Where c0 and z0 are random complex numbers of the form:
z = x + i * y
where x and y are real numbers and i is the imaginary square root -1. The first three images use n = 3, the next one n = 4, the next four n = 5, and the last three n = 6.
z1 = z0 ^ 2 + c0 = z0 * z0 + c0
See Section 2.8 Tumor Cell Growth in “Mathematical Biology – 1: An Introduction” by J. D. Murray pages 72 – 75.
The key equation is give on page 72:
N[t + 1] = r * N[t] * {1 – N[t]}
I had a mentor in my formative years of 1976 – 1985 whose name was Dr. Professor Kenneth Cooper, BS, MS, MCSE, PhD. He supposedly earned his Doctor of Philosophy in Biochemistry at Florida State University and Master of Computer Science Engineering at Auburn University. By my first graduation from LaGrange College on May 31, 1979, Professor Cooper had built by hand an analog computer and a primitive microprocessor computer in a wooden box. I learned how to program both computers. As stated earlier in blog entry by me, I took an Intel 8080 or 8085 microprocessor architecture course taught by Dr. Cooper Spring Quarter of 1979. I was the only student in the class. I learned how to hand assemble assembly language to convert it to machine language and enter it into the microprocessor’s computer memory via a two-digit hexadecimal display and crude keypad. One of my first programs was a countdown from FF in hexadecimal (255 decimal) to 00 Hexadecimal (0 decimal). I had to use a timer and other programming features. Professor Cooper did a lot more for me after graduation much I have written much about our mentor-mentee relationship in previous blog entries. I lost track of Professor Cooper from about 1985 until sometime in June or July 2019. I assumed he was dead until one day or night while I was incarcerated at Pathways Center Second Season, a staff member made the announcement to me that she was married to my Dr. Cooper. She knew the fact that he liked raising honeybees and was a continually active beekeeper. This staff member was Tameka (spelling etc.) who supposedly was inseminated at a sperm bank with one or more of my sperm and gave birth to a child who is now 22 years old and supposedly my child whom I had never met until the summer of 2019. My “child’s” name is pronounced roughly as “Malaysia”. These two revelations had me flabbergasted. I really did not believe that CIA cover story. See I have always felt that Kenneth Cooper was a United States Air Force driver of an A-12 Oxcart (Archangel) aircraft and thus was also an operative in the Central Intelligence Agency. Supposedly Dr. Cooper now flies a helicopter that he and the CIA bought him. I believe his real name is Colonel Kenneth S. Collins. Malaysia was pregnant with supposedly my grandchild. I will write more about Dr. Cooper and company in a later blog entry.
I first implemented Singleton’s sorting algorithm in the Summer of 1979. The programming language was Data General’s version of Dayton BASIC (Beginner’s All-purpose Symbolic Instruction Code). This variant of BASIC was interpretive like C#, Java, and Pascal. Below is my BASIC version and run-times for double precision numbers in an inverted sequence.
Zoom forward to my current computer and C# programming language in 2018.
Simulated firing of a 16 inch by 50 calibers battleship Iowa BB-61’s main artillery. This is the maximum range (24.56 miles)!
