Create an educational fractal animation video starting from a straight line, with the following recursive process: 1. **Initial State**: - Show a horizontal line segment (length L). 2. **Iteration 1**: - Divide the line into two equal segments at its midpoint. - Remove the right segment completely. - Replace the removed segment with a regular octagon: * The octagon's width must exactly match the removed segment's length (L/2). * Place it centered on the original right segment's position. * Orient one side parallel to the original line direction. 3. **Recursion Rule**: - Apply the same process to every new line segment (including all sides of the octagon): a. Divide each segment at its midpoint. b. Remove its right half. c. Replace with a scaled-down regular octagon (width = current segment length / 2). 4. **Visualization Depth**: - Animate 3 full iterations: * Iteration 0: Initial line (blue) * Iteration 1: Octagon replaces right half (red) * Iteration 2: Each octagon side splits → new octagons (green) * Iteration 3: Further subdivision (yellow) **Critical Specifications**: - Use **2D vector animation** with smooth transitions between steps. - Scale octagons precisely: Width(n) = Initial Length / 2ⁿ - Color-code by iteration depth (blue→red→green→yellow). - Add dynamic labels: "Step 0: Initial Line", "Step 1: First Replacement", etc. - End with an overview showing fractal self-similarity.

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Welcome to our exploration of fractals - fascinating geometric patterns that exhibit self-similarity at every scale. Today we'll create a unique fractal starting from a simple line segment. Our recursive rule has three steps: first, divide any line segment at its midpoint. Second, completely remove the right half. Third, replace the removed segment with a regular octagon whose width exactly matches the removed segment's length. This process creates infinite complexity through simple repetition. Now we begin with Step 0, our initial line. Here we have a horizontal line segment of length L, displayed in blue color. This line represents the foundation of our fractal. Watch as we divide this line at its exact midpoint, creating two equal segments of length L over 2. The vertical red indicator shows the division point. We can see the left segment remains, while the right segment - highlighted in the red box - will be completely removed. This removed segment's length, L over 2, determines the width of the octagon that will replace it. Now we move to Step 1, our first replacement. We construct a regular octagon in red color to replace the removed segment. The octagon's width must exactly match the removed segment's length, which is L over 2. Watch as we position the octagon precisely - it's centered on the original right segment's location. Notice how one side of the octagon is oriented parallel to the original line direction, maintaining geometric consistency. The construction circle helps visualize the octagon's regular shape, and the highlighted parallel side demonstrates the proper orientation. This replacement establishes the scaling relationship that will govern all future iterations. We now enter Step 2, the recursive application phase. Here we systematically apply our three-step process to every existing line segment. This includes the remaining left segment in blue and all eight sides of the red octagon. Watch as we identify the midpoint of each segment with green indicators. For each segment, we divide at the midpoint, remove the right half, and replace it with a smaller green octagon. The new octagons have width equal to L over 4, exactly half the size of the previous generation. This demonstrates the fractal's self-similar scaling property, where each iteration creates smaller copies following the same geometric rules. We now reach Step 3, demonstrating the fractal's increasing complexity. We apply our recursive process to all line segments created in the previous iteration. This includes the remaining blue segment, all sides of the red octagon, and all segments from the green octagons. Each replacement creates yellow octagons with width L over 8, continuing our scaling pattern. Notice the exponential growth - what started as a single line now contains dozens of geometric elements. The fractal structure becomes increasingly intricate while maintaining perfect self-similarity at every scale. This demonstrates how simple recursive rules can generate infinite complexity and beautiful mathematical patterns.