This draws a default rectangle, which is a horizontal square:

This draws the square rotated:

You can make anything interactive in the Wolfram Language with Manipulate—for example, this code:

First replace the numeric angle value with a variable named angle:

Then wrap the expression with Manipulate and specify the range of the variable. Manipulate automatically constructs an interface with a slider that controls the value of the angle:

Table makes lists of elements, one for each value of a variable in a specified range. For example, this makes a list of even numbers:

This uses Table to make a stack of rectangles, each one rotated 5 degrees more than the one below it. It doesn’t look like a stack of rectangles because you can’t see their edges:

Make the edges white so you can see the individual rectangles in the stack:

This draws a stack of rectangles:

Make that expression interactive with Manipulate. Replace the numeric angle value with a variable named angle:

Then wrap the expression with Manipulate and specify the range of the angle variable:

The number of squares in this expression is determined by the value 10:

Replace 10 by the variable n, and specify that n goes from 1 to 100 in steps of 1:

This draws a stack of squares rotated in 5-degree increments:

This uses Scale to scale down the squares as they rotate. The scale factor is 1-r/10, which goes from 1 to 0 as r goes from 0 to 10. The effect is to scale the squares from full-sized down to nothing:

Add scaling so that the rectangles get smaller as they rotate. Now you have a complete interface for exploring spiral designs:

Deploy the Manipulate to the Wolfram Cloud, where anyone with a browser can use it:

Click the link in the output to visit the site.

Tell the world about your creation by sharing the link via email, tweet or other message.