Arrays, or Lists of Lists: Elementary Introduction to the Wolfram Language

13	Arrays, or Lists of Lists

We’ve seen how Table can be used to make lists. Now let’s see how Table can be used to create higher-dimensional arrays of values.

Make a list of 4 copies of x:

In[1]:=

Out[1]=

Make a list of 4 copies of a list that contains 5 copies of x:

In[2]:=

Out[2]=

Use Grid to display the result in a grid:

In[3]:=

Out[3]=

You can use Table with two variables to make a 2D array. The first variable corresponds to the row; the second to the column.

Make an array of colors: red going down, blue going across:

In[4]:=

Out[4]=

Show every array element as its row number:

In[5]:=

Out[5]=

Show every array element as its column number:

In[6]:=

Out[6]=

Generate an array in which each element is the sum of its row and column number:

In[7]:=

Out[7]=

Generate a multiplication table:

In[8]:=

Out[8]=

ArrayPlot lets you visualize values in an array. Larger values are shown darker.

Visualize a multiplication table:

In[9]:=

Out[9]=

Generate and plot an array of random values:

In[10]:=

Out[10]=

ArrayPlot also lets you put colors as values:

In[11]:=

Out[11]=

Images are ultimately arrays of pixels. Color images make each pixel have red, green and blue values. Black-and-white images have pixels with values 0 (black) or 1 (white). You can get the actual pixel values using ImageData.

Find the value of pixels in an image of a “W”:

In[12]:=

Out[12]=

Use ArrayPlot to visualize the array of values:

In[13]:=

Out[13]=

The image is of very low resolution, because that’s how Rasterize made it in this case. It’s also white-on-black instead of black-on-white. That’s because in an image 0 is black and 1 is white (like in RGBColor), while ArrayPlot’s default is to make larger values darker.

You can do arithmetic with arrays, just like lists. That means it’s easy to swap 0 and 1 in this array: Just subtract everything from 1, so every 0 becomes 1−0=1, and every 1 becomes 1−1=0.

Find pixel values, then do arithmetic to swap 0 and 1 in the array:

In[14]:=

Out[14]=

The result is black-on-white:

In[15]:=

Out[15]=

Vocabulary

Table[x,4,5]		make a 2D array of values
Grid[array]		lay out values from an array in a grid
ArrayPlot[array]		visualize the values in an array
ImageData[image]		get the array of pixel values from an image