TheDLA vs Population Simulator

TheDLA Cool Science! TheDLA gives you an essence of pattern formation mechanism in nature. Also, it makes very unique attractive images for you. I wrote a brief description about DLA pattern and TheDLA app in following URL. Please read it! https://sites.google.com/site/dueyama/home/thedla “The DLA” stands for ‘The Diffusion Limited Aggregation’, and it is one of the simplest models that makes complex dendritic pattern. Now, we are talking about Science. You see, there are two types of particles on the field. One is the free particle that moves randomly. Another is the fixed particle that does not move. The free particle attaches to cluster of the fixed particles when it reaches around them. Such a simple pattern forming mechanism builds the attractive complex patterns and this very scientific system is applied for you to have funny hairy nose. But first of all, please check the usage. So, you will be able to enjoy not just hairy nose, but the various patterns YOU are going to create. It is quite amazing that such randomness sometimes create forms and patterns you can find only in nature. Please enjoy the patterns and think why such dendritic patterns appear. If you would like to search the web, keywords may be “DLA” and “Dendrite”. http://en.wikipedia.org/wiki/Diffusion-limited_aggregation To start with, there is a single fixed particle at the center of the field when you start. Usage: - Double tap: Put the fixed particles at the point. The size is possible to change in the setting. - Single tap: Remove the fixed particle at the point. - 2 fingers double tap: Remove all fixed particles from the field + etc. - 2 fingers pan: Pan the field. - Long pressed pan: Draw fixed particles like a pen. - Long pressed pan after a tap: Eraser. - You can chose color to paint the branches. - A “g” button toggles the acceleration sensor of the device (only for the device that has the acceleration sensor). The free particles drift to the direction of the gravity. - Can export the image to the photo library, Twitter and Facebook. In addition, the face detection technology in iOS is used to put the fixed particles on eyes position in the photo. When you are in the Anim mode, exporting the image to the photo library make a GIF anim. So, enjoy patterns! Enjoy science!

"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.）