Population Simulator vs Calcu

"Population simulator" is an application to visually see the changes in the population by using "Logistic Map". You can see the change in the population by the Logistic Map by a line graph and colony size. You can observe the variation pattern of population variety by changing slightly the initial value. Logistic Map is not only used in Population Ecology but also considered one of the starting point of Chaos Theory. I developed this app to help people who are studying Population Ecology or Chaos Theory. ＊Logistic Map may not necessarily apply to changes in population of actual organisms, because Logistic Map is a model of a simple change of the population. ■What is Logistic Map? The Logistic Map is the map that is generated from the Logistic Function that has been devised as a variation model of the population of an organism. It is expressed by the following function. X(n+1) = a・X(n)・(1-X(n)) In the above equation, the meaning of each symbol is as follows. ・n:Generation (n=1,2,3,...) ・X(n):Value obtained by normalizing the Population of Generation n-th（0≦X(n)≦1) ・a:Value obtained by normalizing the Reproductive Rates（0≦a≦4) You can calculate the population of the next generation from a population of a certain generation by using this function. In addition, You can predict the variation of the population over the long term by calculating the population of individuals repeatedly in this function. ■Pattern of Logistic Map Logistic map vary widely depending on the value of "a". ・In case (0≦a≦1) : X(n) converges to 0. ・In case (1＜a≦2) : X(n) converges to 1-(1/a). ・In case (2＜a≦3) : X(n) converges to 1-(1/a) while oscillating. ・In case (3＜a≦3.5699456・・・) : X(n) oscillate between the periodic point individual Power of 2 ・In case (3.5699456・・・＜a≦4) : X(n) Change irregularly.（Chaotic region）＊It may become periodically by the value of a. Please try to observe the changes of Logistic Map by changing the various initial values​​. ■Main function of App 1. Simulation of changes in colony size 2. Line graph of changes in population 3. Output CSV file（Need to purchase add-on.） 4. Output Graph Image（Need to purchase add-on.）

Calcu-Logarithm performs calculations and helps user understand logarithms on advanced level: 1. Solves equation "y = log_a(x)” for “y”, “x”, and “a”, with relevant graphs. 2. Explains and illustrates how to compute log_e (x) from Taylor series. 3. Explains and illustrates how to compute log_10 (x) digit by digit (based on M.Goldberg algorithm). 4. Explains and provides proof of log_e definition as the integral of x inverse. 5. Simplifies logarithmic expressions and solves logarithmic equations with polynomials of up to 20th degree. 6. Includes virtual slide rule for multiplication and division. 7. Calculates, explains, and graphs logarithms of complex numbers. Developers welcome any feedback, please write to us at graphmath@aol.com. Please check out our other Math apps.