Step by Step solution about How to resolve the algorithm Archimedean spiral step by step in the Ruby programming language

This Ruby code creates an Archimedean spiral using the Processing library. An Archimedean spiral is a plane curve defined by the parametric equations (r = a + b\theta) and (\theta \ge 0), where (a), (b) are real numbers.

The code starts by setting up the sketch with a title and background color, and translating the origin to the center of the window. It then begins a shape, and iterates over a range of values for theta from 0 to 50π in increments of INCR.

For each value of theta, the code computes the corresponding values of x and y using the parametric equations of the spiral, and adds a curve vertex to the shape. After iterating over all values of theta, the code ends the shape.

The settings method sets the size of the window to 300 pixels by 300 pixels.

Here is a breakdown of the key parts of the code:

• attr_reader :x, :theta: This line defines two accessor methods, x and theta, which can be used to access the instance variables @x and @theta.
• setup: This method is called once when the sketch starts. It sets up the sketch by creating the background, translating the origin to the center of the window, and beginning a shape.
• begin_shape: This method starts a new shape. All subsequent drawing commands will be added to this shape.
• (0..50*PI).step(INCR) do |theta|: This line iterates over a range of values for theta from 0 to 50π in increments of INCR.
• @x = theta * cos(theta / PI): This line computes the value of x for the current value of theta.
• curve_vertex(x, theta * sin(theta / PI)): This line adds a curve vertex to the shape at the point (x, y), where y is computed using the parametric equations of the spiral.
• end_shape: This method ends the shape. All drawing commands after this point will be drawn outside of the shape.
• settings: This method sets the size of the window to 300 pixels by 300 pixels.

INCR = 0.1
attr_reader :x, :theta

def setup
  sketch_title 'Archimedian Spiral'
  @theta = 0
  @x = 0
  background(255)
  translate(width / 2.0, height / 2.0)
  begin_shape
  (0..50*PI).step(INCR) do |theta|
    @x = theta * cos(theta / PI)
    curve_vertex(x, theta * sin(theta / PI))
  end
  end_shape
end

def settings
  size(300, 300)
end