Population Simulator
Study Ecology By Logistic Map
免費Offers In-App Purchases
2.0for iPhone, iPad and more
Age Rating
Population Simulator 螢幕截圖
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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最新版本2.0更新日誌
Last updated on 2023年04月25日
歷史版本
・Supported iOS16.
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Version History
2.0
2023年04月25日
・Supported iOS16.
1.9
2021年09月30日
Support iOS15.
1.8.1
2020年12月21日
Updated advertising SDK.
1.8
2020年10月08日
Support iOS14.
1.7
2019年10月07日
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
2018年12月04日
Support iPad Pro (3rd gen) screen size.
1.6
2018年10月03日
Support iOS12.
1.5.1
2017年11月10日
Support iPhone X screen size.
1.5
2017年10月10日
Support iOS11.
1.4
2017年08月23日
Support iOS10
1.3
2016年07月27日
Support iOS9
1.2
2015年04月09日
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
2014年12月19日
Updated Ad SDK.
1.1
2014年10月16日
1.0
2014年05月29日
Population Simulator FAQ
點擊此處瞭解如何在受限國家或地區下載Population Simulator。
以下為Population Simulator的最低配置要求。
iPhone
須使用 iOS 15.0 或以上版本。
iPad
須使用 iPadOS 15.0 或以上版本。
iPod touch
須使用 iOS 15.0 或以上版本。
Population Simulator支持日文, 英文
Population Simulator包含應用內購買。 以下為Population Simulator應用內購買價格清單。
Add Output Function
$0.99
