Continuity of Energy–Frequency Relations

Overview

A clean, premium‑style animation that visually demonstrates the logical progression of related physics equations:
$E = mc^2 \rightarrow E = hf \rightarrow mc^2 = hf \rightarrow f = \frac{mc^2}{h} \rightarrow f_{C} = \frac{mc^2}{h}$.
The viewer sees each symbol move and re‑arrange rather than being replaced, emphasizing continuity.

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Phases

#	Phase Name	Duration	Description
1	Intro – $E = mc^2$	~2 s	The equation $E = mc^2$ appears centered on a pure black background and holds.
2	Add $E = hf$	~2 s	The second equation $E = hf$ fades in directly below the first, both remain centered.
3	Merge to $mc^2 = hf$	~2 s	The two leading "E" symbols fade out, "mc^2" slides leftward to center‑left, "hf" slides rightward to center‑right, and an equals sign appears between them, forming $mc^2 = hf$.
4	Rearrange to fraction form	~2 s	"mc^2" stays, "h" separates from "f", "f" moves left of the equals sign, "h" moves beneath "mc^2", a clean horizontal fraction bar is drawn, yielding $f = \frac{mc^2}{h}$.
5	Add subscript C	~3 s	A subscript "C" is smoothly attached to the "f", producing the final equation $f_{C} = \frac{mc^2}{h}$.
6	End hold	~2 s	The final equation remains on screen for a brief pause before the scene ends.

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Layout

┌─────────────────────────────────────────────┐
│                                             │
│                MAIN (equations)            │
│                                             │
└─────────────────────────────────────────────┘

Area Descriptions

Area	Content	Notes
Main	All equations and moving symbols, rendered in bold upright white LaTeX typography.	Uses the full 1920×1080 frame; no additional caption band needed.

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Notes

• Background: pure black (RGB 0,0,0). Text color: pure white, bold, upright, non‑italic LaTeX fonts.
• All motions use slow, smooth professional ease‑in/ease‑out curves; no abrupt jumps.
• Fade‑out of the two "E" symbols lasts ~0.5 s and is the only opacity change.
• Symbol movements are continuous: each element travels along a straight line at constant speed within its easing profile.
• The fraction bar is drawn as a thin white line that appears simultaneously with the positioning of "h" beneath "mc^2".
• No decorative text, camera motion, particles, neon, glow, bouncing, or flashy transitions.
• Assumptions made: total scene length ≈13 s (well under the 30 s limit); a single Scene class suffices; no persistent caption/footer is required.
• All LaTeX symbols are kept sharp by rendering at the native resolution of the 1080p canvas.