To construct a logarithmic spiral using golden rectangles where the initial rectangle has sides measuring 4 units, you can follow these steps:

Step 1: Define the Golden Ratio

The golden ratio (denoted by $\phi$) is approximately 1.618. This value governs the relationship between the lengths of the sides of a golden rectangle. Specifically, the ratio between the longer side (denoted as $l$) and the shorter side (denoted as $s$) of a golden rectangle is:

$\frac{l}{s} = \phi$

Step 2: Construct the Initial Golden Rectangle

Given that one side of the rectangle measures 4 units, let's call this side $s = 4$. Using the golden ratio, the other side of the rectangle, $l$, can be calculated as:

$l = \phi \cdot s = 1.618 \cdot 4 = 6.472 \, \text{units}$

So, the dimensions of the initial golden rectangle are 4 units by 6.472 units.

Step 3: Subdivide the Rectangle into Smaller Golden Rectangles

Inside the original rectangle, you can draw a square with sides equal to the shorter side of the rectangle (4 units). This will leave a smaller golden rectangle inside, with dimensions 4 units by approximately 2.472 units (since