TheDLA vs Drawing with Math

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!

Our “Drawing with Math (Vector and Pixel Art)” app combines two main components: * uniquely versatile image editors, * various methods of linear transformations of both user-entered and system images. Image editors are available in vector and pixelated forms. The editors offer such options as: * free drawing, * entry of all standard shapes, * entry of regular Cartesian, polar, or parametric function into image editor. List of several visually appealing functions is provided. The App stores 10 most recent user entries for each type. Vector images can be linearly transformed in a variety of user-defined ways: * 2x2 matrix, * eigenvalues and eigenvectors, * rotation by degree, * reflection across a given vector. Pixelated images can be compressed by segments to user-selected rank. Mathematical context for the above is provided, whenever possible. Explanation of image compression algorithms requires significant understanding of Linear Algebra, and is available in our “Matrix Solver Step by Step” app. Several bonus images with animations and editable greeting cards are also available. Suggestions and any other feedback are welcome! Write to us at graphmath@aol.com.