Guide

Here you’ll learn step by step how Math-Nodes works. Use the table of contents to jump to a topic — or simply scroll through the whole guide.

In Math-Nodes you work with cards. You connect them with cables so that values or text can “flow” from one card to the next.

To help you find your way quickly, the cards are color-coded: Orange means input (you set something), Green means a machine (it processes something), Blue means output (you see or hear the result).

Important: Only Word Machines, Function Machines, and the Operation Machine are called “machines” here. Everything else is simply called a card.

Tip: In many tasks the right cards are already on the workspace. Most of the time you only need to set values, move cards, and draw the correct cables.

The workspace

On the workspace you build your wiring. You move cards, connect them with cables, and you can add new cards.

Go to the steps

Card types and colors

There are three card types. The colors help you quickly see what a card does.

Input cards (orange): Independent variable card, parameter card, piano card (in the “Listen to functions” chapter), and text input card.
Machines (green): Function machines (function card), operation machine (operation card), and word machines.
Output cards (blue): Graph card, equation card, value card, audio card, and the text output card (for word machines).

Cables are drawn from the output of one card to the input of another. One output can feed multiple cables, but each input can only have one cable.

Move cards

Click a card and drag it to the right place. On a tablet, you can move it with your finger.

Connect cards

You connect cards with cables. Drag a cable from the blue output of one card to the orange input of another card.

Remember: An output can have multiple cables. Each input can only have one. If a cable is already connected, grab it at the end and reconnect it.

Add cards

New cards can be added like this:

Double-click an empty spot: add a card.
Double-click a card: replace the card.
Or use the “New card” button.

Delete a card with Backspace or via the menu.

The menu

Each workspace in Math-Nodes has its own menu with useful functions.

In the menu you’ll find, for example: fullscreen, save as image, save/load, clear all, new card, zoom, arrange cards, and delete card.

Fullscreen: Puts the view into fullscreen mode so you have more space to work with your machines. To exit fullscreen, press the Esc key or click the fullscreen button again.
Save as image: Saves the current view of the workspace as an image file. This is useful for documenting or sharing your work.
Save: Saves your workspace as a file on your computer. This way, you can continue later or share your wiring with others.
Load: Loads a file you previously saved. This way, you can continue working on a task or prepare your own.
Clear all: Removes all cards from the workspace. You’ll get a safety prompt first.
New card: Depending on where you are in Math-Nodes, you can select word machines or function machines. On Create Your Own Tasks you’ll find a blank workspace. You can also access this menu by double-clicking (empty = add, on card = replace). To close, click the top right.
Zoom: Zooms in or out on the workspace. This is useful if you have a small display.
Arrange cards: The cards are automatically positioned on the workspace for optimal overview. The spacing between cards is maximized but their relative positions are mostly kept. If you resize the window or switch in or out of fullscreen, this happens automatically. You can also use this if you accidentally moved a card off the workspace.
Delete card: Removes the selected card from the workspace. This is useful if you no longer need a card.

Word Machines

Word Machines work with text. You enter text, place one or more word machines in between, and read the new text at the end. Spaces and special characters stay the same. Only letters (A–Z and a–z) are changed.

Word machines in detail

Here you can see what each word machine does. As always, spaces and special characters stay the same — only letters (A–Z and a–z) are changed.

Text input: With the text input card you enter text that other cards can process. Example: "Hello world".
Text output: The text output card shows the text after it has been processed by other cards. Example: "Hello world".
Alphabet countdown: Replaces each letter with the previous one in the alphabet. Example: "BCD" becomes "ABC".
Reverse: Reverses the entered text. Example: "Hallo" becomes "ollaH".
Vowel swap: Replaces all vowels (A, I, O, U) with E. Example: "Hallo" becomes "Helle".
No vowels: Removes all vowels (A, E, I, O, U). Example: "Hallo Welt" becomes "Hll Wlt".
Swap neighboring letters: Swaps every two neighboring letters. Example: "Hallo" becomes "aHlol".
Skip every second letter: Skips every second letter. Example: "SPIEL" becomes "SIL".
Alphabet jump: Replaces each letter with the one two steps ahead in the alphabet. Example: "ABC" becomes "CDE".
Remove double letters: Removes the second letter if two identical letters follow each other. Example: "SCHWIMMEN" becomes "SCHWIMEN".
Alternating vowels: Replaces every E alternately with A, I, O, and U. Example: "Essen" becomes "Assin".
Letter ballet: Shifts every three consecutive letters cyclically by 1 position. Example: "ABCDEF" becomes "BCDAEF".
Vowel dance: Replaces every vowel with the next vowel in the alphabet. Example: "Hallo" becomes "Helle".
Vowelium: Replaces every vowel with the previous vowel in the alphabet. Example: "Hallo" becomes "Hillu".
Double consonants: Doubles every consonant in a word. Example: "SPIEL" becomes "SSPPIELL".
Double everything: Each letter is output twice. Example: "SCHWIMMEN" becomes "SSCCHHWWIIMMMMEENN".
Front and back: Takes a word alternately from the start and end of the text. Example: "Eins Zwei Drei Vier" becomes "Eins Vier Zwei Drei".

Function Machines

In Function Machines you work with numbers and functions you know from school. You connect inputs, machines, and outputs — and view the result as a graph, equation, value, or audio.

Card types (input, machine, output)

Input cards are at the start of a wiring (e.g., independent variable, parameter, text input, piano).
Machines (green cards) process the input: function machines (function card), operation machine (operation card), and word machines.
Output cards are at the end and show the output in a form (graph, equation, value, audio, text output).

When connecting, it’s always: output → input. Multiple cables can leave an output, but each input only takes one.

Chain functions

When chaining, one machine comes after the next. The output of the first machine goes into the second machine.

Start with an independent variable card (e.g., x).
Connect it to one or more function machines.
Attach an output card (e.g., value or graph).

Tip: If you animate the independent variable, you’ll often see a moving point in the graph.

Combine functions (Operation Machine)

With the operation machine you can add, subtract, multiply, or divide two functions.

Connect the two functions on the left to the two inputs.
The output comes out on the right — like with all other cards.

Use parameters

Parameters are like “knobs” for a function machine. You set a value and immediately see how the function changes.

Create a parameter (e.g., a) and set a value.
Write the parameter name into the function formula (e.g., f(x)=a·x).
Connect the parameter to the matching red input of the function machine.

Tip: Change the parameter and watch how the graph or value changes.

Listen to functions (audio / piano)

With the audio card you can listen to some functions. Often t (time) is the input. If t is animated, a tone is produced.

Build a periodic function (e.g., sine) and connect it to the audio card.
Switch Tone On/Off in the audio card.
Start the animation of time t.

Cards in detail

Independent variable

Here you set the name (e.g., x or t) and a value. In many tasks you can animate the value.

Parameter

Parameters are “knobs” for functions. You can create several parameters and change their values.

Function machine (function card)

The function machine takes in a value and outputs a new value — according to the function formula.

Make sure the variable in the formula matches your independent variable card (e.g., x or t).

Right-click (or two-finger tap) lets you select commonly used formulas or show/hide the free input.

Operation machine (operation card)

Combines two inputs using +, −, ·, or ÷ and outputs the result.

Right-click lets you show/hide the button in the card.

Value

Shows the current value of the function.

Equation

Shows the function as an equation.

Right-click lets you save the current equation or delete a saved one.

Graph

Shows the graph of the function.

Right-click lets you, among other things, save/delete the top function and toggle background (white/black) and drawing.

Audio

Outputs the function as sound. This is an output card.

Info for advanced users

These features are especially useful if you want to create your own tasks or document your results.

Minimize widgets / cards

You can minimize a card using the icon at the top left. Then only the title remains visible. This helps keep large wirings organized.

Document your wiring (image / file)

Save as image: Saves the view as an image (e.g., for submission or screenshot).
Save / Load: Saves your workspace as a file. Later you can load it again or share it with others.

Email

Nicolas.Regel@TU-Dresden.de

Phone

0351 46332074