Fibonacci Tree Generator
The Fibonacci Sequence in Fractal Trees
In the world of mathematics and nature, the Fibonacci sequence is more than just a series of numbers. It also plays a fascinating role in the creation of fractal trees. This code demonstrates how the Fibonacci sequence influences the growth of a tree.
Fibonacci Influence
The Fibonacci sequence appears when the tree branches divide. At each branching point, the tree splits into two branches, one turning left and the other turning right. The angle at which the branches divide is set to 45 degrees (π/4). The number of branches generated at each level of recursion follows the Fibonacci sequence.
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The first branch divides into two branches.
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The second level has three branches.
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The third level has five branches.
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The fourth level has eight branches.
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And so on, following the Fibonacci sequence: 1, 2, 3, 5, 8, 13, 21...
As you explore this fractal tree, you'll notice the beauty of Fibonacci numbers in nature. The branching pattern is reminiscent of the graceful growth seen in trees and plants. The fractal tree is not just a mathematical construct; it's a reminder of how nature's design often reflects the elegance of mathematical patterns.
