Damascus is a Unity-based software for graphing and visualizing complex functions, derivatives, and integrals.
Step 1: Download and install the latest version of Unity Hub and the Unity editor.
Step 2: Download the latest version of Damascus, and unzip the file.
Step 3: At the top of Unity Hub, click "Add" and select the unzipped file.
Step 4: That's it! Just run the program, and you are good to go!
- All functions are supported! Use premade functions in "System.Numerics.Complex", or write your own!
- Easily input any desired value, and receive the output, derivative, and integral (from the starting value) at that point.
- Along with direct inputs, Damascus allows you to generate maps of your chosen function, enabling you to visualize the shape of functions and identify zeroes.
- Two by two matrices are supported, letting you see the effect of transformations on any two dimensional vector.
Once the program is open in the Unity editor, select the "Damascus" scene in the "Scenes" folder under "Assets". Then click the play button at the top of the editor, and the program will run.
Open the "Funcs" file in the "Scripts" folder under "Assets" with a code editor (I use Visual Studio). Inside "Funcs", there is a method named "Function", which contains the assignment you will change. Below the commented lines, there is an assignment that looks like "Complex output = (function)". Simply change "(function)" to whatever function you want to graph, using "z" as the input variable. Most functions can be found in the "Complex" class, but any arithmetic operator will work too. If the "Complex" class does not contain your desired function, feel free to program it yourself!
A tutorial is avalible here: https://www.youtube.com/watch?v=oCwgYL-QqKc
Inside the "Damascus" scene, the game object named "Code" contains all the settings currently implemented. These settings include toggling the derivative and integral calculations, and calibrating the function mapping capability.
Damascus allows the mapping of functions along the complex plane. By default, Damascus converts the output of a function into a color based on the HSV color format. The conversion uses the argument (degrees in standard position) of the output, and converts that to a hue. Pure red is at 0°, pure green is at 120°, and pure blue is 240°. The saturation of the color is based on the magnitude of the output. Lastly, zeros are displayed with black, the blacker it is, the closer it is to zero. If you toggle RGB, you instead choose custom colors for a high real and imaginary value, plus a color for proximity to zero.
Left Click: Left clicking smoothly brings the input selector to the position of your mouse.
Arrow Keys: Clicking any arrow key will move the input selector 0.001 units in its corresponding direction.
Scroll Wheel: Scrolling will zoom in or out, adjusting the scale of the input and output space.
Ctrl: Holding ctrl while pressing the arrow keys will cause the input selector to smoothly move in the arrow key's corresponding direction.
Shift: Holding shift will multiply any movement triggered by the arrow keys by a factor of 5.
Alt: Holding alt will lock the input selector to the unit circle.
Enter: Clicking enter will reset the scale to 1, and return the input selector to the origin.
X: While holding x, type in any real coordinate you want your input selector to land on, once you are done typing, release x and the input selector will move to the desired real coordinate.
Y: While holding y, type in any imaginary coordinate (don't add "i" at any point) you want your input selector to land on, once you are done typing, release y and the input selector will move to the desired imaginary co-ordinate.
I: Clicking i will toggle between controlling the input selector, or the integral start point selector.
R: Clicling r will recalculate the heat map, applying any changes made under the "Code" object of the project. Only click r if you make changes while the program is running, any changes made before running the program are automatically applied.