Population Simulator -Manual-

1.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.

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2.Screen Description

Menu Button

Display following contents.
- Manual
- Settings
- Graph Image Output
- Add-on purchase
Display area

Colony and Graphs are displayed here.
Tab Button

Switch between "Colony", "Dynamic Graph" and "Static Graph". Reference
Start Button

Start Simulation. Become Stop Button during Simulation.
Reset Button

Stop Simulation and Reset the value.
Edit Button

Show "Parameters Edit" Screen. Reference

Type Description

Colony

Population is represented by the size of the Colony. When you start simulation, the size of the colony will change depending on the population.

Dynamic Graph

Population is represented by the Line Graph. When you start simulation, Line Graph will display the current population.

Static graph

Show Line Graph of the range of (0 ≦ n ≦ 500). You can scroll the graph horizontally by Flick.

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3.Start Simulation

When you press "Start" Button, simulation that is based on the current parameters will be start.

You can pause the simulation by "Stop" Button.

You can reset the values by "Reset" Button.

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4.Parameters Edit

When you press "Edit" button, "Parameters Edit" Screen will be shown.
You can edit parameters in this screen.

Parameters Edit Screen

Initial Population "X(0)"

Input field of Initial Population "X(0)".
Reproduction Rate "a"

Input field of Reproduction Rate "a".
Sample

When you select sample, parameters indicating a specific pattern will be set.
Save Button

Save parameters and back to the previous page.
Back Button

Back to the previous page.

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5.Settings

When you select "Settings" from "Menu" Button, "Settings" Screen will be shown.

Settings Screen

Speed of generation change

you can change the speed of generation change(speed of simulation).
Save Button

Save parameters and back to the previous page.
Back Button

Back to the previous page.

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6.Graph Image Output

You can output Graph image that is range of (0 ≦ n ≦ 100) by selecting "Graph Image Output" from "Menu" Button.

＊If you want to use this function, you need to purchase the Add-on. Reference

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7.Add-on purchase

You will be able to output Graph Image and hide advertising by purchasing Add-on.

How to purchase Add-on

If you want to see In-App Purchase Screen, Please select "Advertising Hide" from Home Screen Menu Button.
If you want to purchase the add-on, press the "Purchase" button in "In-App Purchase Screen" after you checked the description and price.

※You need Apple ID, if you want to purchase the add-on.

※If you want to re-install after purchase or you want to use the add-on in other iOS device after purchase, please push restore button. If you perform a restore, please use the same AppleID at the time of purchase.