Population Simulator
Study Ecology By Logistic Map
FreeOffers In-App Purchases
2.0for iPhone, iPad and more
Age Rating
Population Simulator Screenshots
About Population Simulator
"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.）
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.）
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What's New in the Latest Version 2.0
Last updated on Apr 25, 2023
Old Versions
・Supported iOS16.
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Version History
2.0
Apr 25, 2023
・Supported iOS16.
1.9
Sep 30, 2021
Support iOS15.
1.8.1
Dec 21, 2020
Updated advertising SDK.
1.8
Oct 8, 2020
Support iOS14.
1.7
Oct 7, 2019
1. Support iOS13.
2. Support Dark Mode on iOS13.
3. Support screen rotation and multitasking on iPad.
2. Support Dark Mode on iOS13.
3. Support screen rotation and multitasking on iPad.
1.6.1
Dec 4, 2018
Support iPad Pro (3rd gen) screen size.
1.6
Oct 3, 2018
Support iOS12.
1.5.1
Nov 10, 2017
Support iPhone X screen size.
1.5
Oct 10, 2017
Support iOS11.
1.4
Aug 23, 2017
Support iOS10
1.3
Jul 27, 2016
Support iOS9
1.2
Apr 9, 2015
Added CSV file output function.
＊If you want to use this function, you need to purchase the Add-on.
＊If you want to use this function, you need to purchase the Add-on.
1.1.1
Dec 19, 2014
Updated Ad SDK.
1.1
Oct 16, 2014
1.0
May 29, 2014
Population Simulator FAQ
Click here to learn how to download Population Simulator in restricted country or region.
Check the following list to see the minimum requirements of Population Simulator.
iPhone
Requires iOS 15.0 or later.
iPad
Requires iPadOS 15.0 or later.
iPod touch
Requires iOS 15.0 or later.
Population Simulator supports English, Japanese
Population Simulator contains in-app purchases. Please check the pricing plan as below:
Add Output Function
$0.99
