# Exploding Dots in the Wolfram Language—Another Tutorial

Exploding Dots in the Wolfram Language—Another Tutorial

In this tutorial, you will experience Exploding Dots the Wolfram way. Using the built-in functions available in the Wolfram Language, you can create your own interactive illustrations based on the Exploding Dots curriculum. In this workbook, we demonstrate how to create a base machine and then move on to the four basic arithmetic operations—addition, subtraction, multiplication and division—and conclude with some weird and wonderful explorations.

Before you can explore all that, this section will provide an introduction to the Wolfram Language.

Let's try to do something simple first. Click the line here and press + :

NOTE: When you execute this line of code, a dialog window will open up asking to execute all Initialization cells. Click “YES”.

Before you can explore all that, this section will provide an introduction to the Wolfram Language.

Let's try to do something simple first. Click the line here and press + :

NOTE: When you execute this line of code, a dialog window will open up asking to execute all Initialization cells. Click “YES”.

In[]:=

1+2+3

Out[]=

6

You should have gotten the output 6.

## Functions

Functions

All calculations in Mathematica are done by calling functions.

You can think of each function as a box. Into each box we put arguments, and then the box spits out a result.

You can think of each function as a box. Into each box we put arguments, and then the box spits out a result.

## Evaluate the Following Examples

Evaluate the Following Examples

(Click next to the inputs, hold down and press .)

In[]:=

Divide[100,10]

Out[]=

10

In[]:=

Expand[(a+b)^2]

Out[]=

a+2ab+b

2

2

In[]:=

ContourPlota+2ab+b,{a,-8,8},{b,-8,8}

2

2

Out[]=

## Code Initialization -- Do not edit.

Code Initialization -- Do not edit.

#### Defining the Functions That Make the Below Possible

Defining the Functions That Make the Below Possible

This looks like a long and intimidating function definition—but in the world of programming languages, this is one of the shortest and most elegant ways to create visualizations of this kind.

There are learning resources at the bottom of this notebook that will help you get started with creating your own powerful applications. For now, go to the Examples and Demonstrations section below.

There are learning resources at the bottom of this notebook that will help you get started with creating your own powerful applications. For now, go to the Examples and Demonstrations section below.

In[]:=

ClearAll["Global`*"]

#### Defining a “Machine”

Defining a “Machine”

In[]:=

toMachine[n:(___Integer|{___Integer}...)]:={n}