Question
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)
Responses
16
16
8
8
32
32
4
4
Remaining Attempt
Responses
16
16
8
8
32
32
4
4
Remaining Attempt
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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**
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**
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