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Consider the following statements with reference to the fractal pattern:
1. It is a pattern which is infinitely complex and self-similar across different scales.
2. Its examples include designs of human fingerprints and stumps of trees.
Which of the statements given above is/are correct?
- a)1 only
- b)2 only
- c)Both 1 and 2
- d)Neither 1 nor 2
Correct answer is option 'C'. Can you explain this answer?
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Consider the following statements with reference to the fractal patter...
Fractal Patterns
Fractal patterns are intricate and complex patterns that exhibit self-similarity across different scales. They are characterized by the repetition of similar patterns at varying levels of magnification.
Statement Analysis
Statement 1: It is a pattern which is infinitely complex and self-similar across different scales.
- This statement is correct as fractal patterns display infinite complexity and self-similarity across scales, meaning that the same pattern repeats at different levels of magnification.
Statement 2: Its examples include designs of human fingerprints and stumps of trees.
- This statement is also correct as examples of fractal patterns can be found in nature, such as the intricate designs of human fingerprints and the branching patterns of tree stumps.
Therefore, both statements 1 and 2 are correct in describing fractal patterns. These patterns are not only fascinating in their complexity but also have practical applications in various fields such as mathematics, art, and technology.
Fractal patterns are intricate and complex patterns that exhibit self-similarity across different scales. They are characterized by the repetition of similar patterns at varying levels of magnification.
Statement Analysis
Statement 1: It is a pattern which is infinitely complex and self-similar across different scales.
- This statement is correct as fractal patterns display infinite complexity and self-similarity across scales, meaning that the same pattern repeats at different levels of magnification.
Statement 2: Its examples include designs of human fingerprints and stumps of trees.
- This statement is also correct as examples of fractal patterns can be found in nature, such as the intricate designs of human fingerprints and the branching patterns of tree stumps.
Therefore, both statements 1 and 2 are correct in describing fractal patterns. These patterns are not only fascinating in their complexity but also have practical applications in various fields such as mathematics, art, and technology.
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Consider the following statements with reference to the fractal patter...
Recently, an international team of researchers’ discovered first fractal molecule in nature.
- It is a never-ending pattern which is infinitely complex and self-similar across different scales.
- In essence, a fractal is a pattern that repeats forever, and every part of the fractal, regardless of how zoomed in or zoomed out you are, it looks very similar to the whole image.
- They are created by repeating a simple process over and over in an ongoing feedback loop.
- Fractals are distinct from the simple figures of classical, or Euclidean, geometry—the square, the circle, the sphere, and so forth.
- Some of the more remarkable examples of such patterns include the design of human fingerprints, the stumps of trees, in the shells of snails, the system of human veins, the network of rivers as seen from high up, the splitting of veins in a plant leaf, the edges of a snowflake etc.
- They are capable of describing many irregularly shaped objects or spatially nonuniform phenomena in nature, such as coastlines and mountain ranges.
- Applications: Fractals are useful in modeling structures (such as eroded coastlines or snowflakes) in which similar patterns recur at progressively smaller scales, and in describing partly random or chaotic phenomena such as crystal growth, fluid turbulence, and galaxy formation.
Hence both statements are correct.
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Consider the following statements with reference to the fractal pattern:1. It is a pattern which is infinitely complex and self-similar across different scales.2. Its examples include designs of human fingerprints and stumps of trees.Which of the statements given above is/are correct?a)1 onlyb)2 onlyc)Both 1 and 2d)Neither 1 nor 2Correct answer is option 'C'. Can you explain this answer?
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