How many lines will be in the fourth stage of the Cantor dust fractal? The first stage is a single solid line. The second stage has the middle third removed and has two solid lines.(1 point)

Question

Responses

16
16

8
8

32
32

4
4
Remaining Attempt

Answer 1

The Cantor dust fractal starts with a single line segment in the first stage. In each subsequent stage, the middle third of each line segment is removed.

Here's how the number of line segments evolves:

• Stage 1: 1 line segment
• Stage 2: The middle third is removed from the single segment, resulting in 2 line segments.
• Stage 3: Each of the 2 line segments from stage 2 has its middle third removed, which gives us \(2 \times 2 = 4\) line segments.
• Stage 4: Each of the 4 line segments from stage 3 has its middle third removed, yielding \(4 \times 2 = 8\) line segments.

Therefore, in the fourth stage of the Cantor dust fractal, there will be 8 lines.

Answer: 8