Animation Specification: Sieve of Eratosthenes (Primes up to 50)

Animation Description and Purpose

Visualize the Sieve of Eratosthenes algorithm to find all prime numbers up to 50. The animation will demonstrate how composite numbers are systematically eliminated, leaving only primes.

Mathematical Elements

• Range: Numbers from 2 to 50 (inclusive).
• Primes up to 50: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.
• Algorithm Steps:
  1. Start with the first unmarked number $p$ (initially 2).
  2. Mark all multiples of $p$ (excluding $p$ itself) as composite.
  3. Repeat until $p^2 > 50$.

Visual Elements

Grid Layout

• Numbers: Displayed in a 5x10 grid (5 rows, 10 columns) for clarity.
• Number Styling:
  • Unmarked Numbers: White text on a dark gray background (hex: #333333).
  • Primes: Bold, bright green text (hex: #00FF00) on a dark gray background.
  • Composite Numbers: Faded red text (hex: #FF6B6B) on a dark gray background.
  • Current Prime $p$: Highlighted with a yellow border (hex: #FFFF00).
  • Multiples Being Marked: Flash briefly in bright red (hex: #FF0000) before fading to composite color.

Animation Objects

• Grid: A rectangular grid of squares, each containing a number from 2 to 50.
• Highlight Circle: A yellow circle that moves to the current prime $p$.
• Strikethrough Lines: Red lines that appear over multiples of $p$ as they are marked.

Animation Timing and Transitions

• Total Duration: ~25 seconds.
• Step-by-Step Breakdown:
  1. Initial Setup (0-2s):
     • Numbers 2 to 50 appear sequentially in the grid (0.1s per number).
  2. Sieve Process (2-20s):
     • For each prime $p$ (2, 3, 5, 7):
       • Highlight $p$ with a yellow circle (0.5s).
       • Flash and mark multiples of $p$ (0.3s per multiple, staggered).
       • Pause briefly (0.5s) after marking all multiples of $p$.
  3. Final Primes (20-23s):
     • All remaining unmarked numbers (primes) change to bright green.
  4. Conclusion (23-25s):
     • A brief flash of all primes to emphasize the result.

Camera Angles and Perspectives

• Static Camera: Centered on the grid with a slight zoom to ensure all numbers are visible.
• No Movement: The camera remains fixed to avoid distraction.

Additional Details

• Number Spacing: Evenly spaced in the grid with minimal padding.
• No Text Overlays: All information is conveyed visually through colors and animations.
• Smooth Transitions: Use easing functions for highlights and flashes to avoid abrupt changes.

Default Assumptions

• If no clarification is provided, the animation will use the grid layout and color scheme described above.
• The sieve will proceed for primes $p$ where $p^2 \leq 50$ (i.e., $p = 2, 3, 5, 7$).