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A fractal pattern is created in a square, beginning with 9 identical squares arranged in a plus sign pattern. At each step, every blue square that borders blue on exactly one edge is replaced with the plus sign pattern from the first step.
As this pattern continues indefinitely, what fraction of the larger square is shaded blue:
5/27, 2/9, 7/27, 8/27???
ever hear of google?
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A fractal pattern is created in a square, beginning with 9 identical squares arranged in a plus sign pattern.
and you will find answers.
They are all identical. There is not a larger square. They are all the same hue of blue
To determine the fraction of the larger square that is shaded blue as the pattern continues indefinitely, we need to analyze how the pattern evolves.
Let's start by observing the first step of the pattern. We have nine identical squares arranged in a plus sign pattern. In this initial step, the fraction of the larger square that is shaded blue is 5/9 because five out of the nine squares are shaded blue.
Now, let's consider the second step. Every blue square that borders a blue square on exactly one edge is replaced with the plus sign pattern from the first step.
If we look closely, we can see that there are four blue squares on the edges of the larger square that meet this condition. These four blue squares will be replaced by the plus sign pattern. Therefore, the number of blue squares after the second step will be 5 (from the first step) plus 4 (newly added blue squares) equals 9.
So, the fraction of the larger square that is shaded blue after the second step will be 9/9, which simplifies to 1/1.
If we continue this process for further steps, we can see that the number of blue squares remains constant after the second step. Therefore, the fraction of the larger square that is shaded blue as the pattern continues indefinitely is 1/1, which simplifies to 1.
Therefore, the correct answer to the given question is 1.