The Physics of Suika Merge Games: Circle Packing, Restitution Impulses & Chain Combos
What makes Suika-style physics merge games so endlessly absorbing compared to static grid puzzles like 2048? In a grid game, tiles sit still until you swipe; in Suika Physics Drop, every sphere is a live 2D rigid body governed by **mass ($m \propto r^2$)**, **translational velocity**, **angular rolling momentum ($\omega$)**, and **elastic restitution ($e$)**. A single merge at the bottom of the jar expands in radius, firing an outward shockwave impulse that can set off a 4-step cascading chain reaction across the entire container.
How to Play & Use the Built-In Powerups
- Aim & Drop (`Mouse Move / Touch Drag` + `Click / Spacebar` or `A / D` Keys): Slide the cute pastry claw across the top of the glass jar. Use the dotted aim laser to line up bank shots off curved spheres below. Only Tiers 1 through 5 spawn in the dropper claw!
- Switch Between 3 Complete 11-Tier Theme Packs Anytime: Click the top ribbon to transform every sphere inside the jar between **🍉 Kawaii Orchard Fruits**, **🎂 Patisserie Cafe Desserts**, and **🪐 Cosmic Solar System Planets** without losing your current game progress.
- Trigger the Seismic Shake Jar Powerup (`S` Key or `📳 Shake Jar`): Every merge adds +15% to your Shake Meter. When charged, triggering a shake jostles the jar horizontally and vertically, settling loose balls into lower gaps and connecting blocked pairs.
- Use the Magic Upgrade Wand (`U` Key or `✨ Upgrade Lowest Ball`): Once per full Shake charge, tap the Upgrade Wand to automatically evolve the smallest troublesome Tier 1–2 ball buried at the bottom of your jar into the next tier!
2D Rigid-Body Circle Collision Impulse & Merge Conservation Equations
d = sqrt( (x_B - x_A)² + (y_B - y_A)² ), δ_overlap = (r_A + r_B) - d, n_hat = (x_B - x_A, y_B - y_A) ÷ d
2. Normal Collision Impulse Magnitude J_n with Coefficient of Restitution e (Mass m_i ∝ r_i²):
v_rel_n = (v_B - v_A) · n_hat, J_n = -(1 + e) · v_rel_n ÷ ( (1 ÷ m_A) + (1 ÷ m_B) )
3. Tier-k Merge Score Progression & Area Conservation (k ∈ [1, 11]):
Score(k) = k × (k + 1) × 5 [Tier 1 Merge = +10 pts ... Tier 10→11 Suika Merge = +550 pts!]
Complete 11-Tier Evolution Chart Across All 3 Theme Packs
| Tier # | 🍉 Pack 1: Kawaii Orchard | 🎂 Pack 2: Patisserie Cafe | 🪐 Pack 3: Cosmic Planets | Sphere Radius | Merge Points |
|---|---|---|---|---|---|
| Tier 1 (Drop) | 🍒 Cherry | 🫐 Blueberry | ☄️ Pluto | 16 px | +10 PTS |
| Tier 2 (Drop) | 🍓 Strawberry | 🍬 Pink Macaron | 🌑 Mercury | 22 px | +30 PTS |
| Tier 3 (Drop) | 🍇 Grapes | 🍓 Mochi Daifuku | 🔴 Mars | 29 px | +60 PTS |
| Tier 4 (Drop) | 🍊 Dekopon Citrus | 🧁 Cupcake Swirl | 🌕 Venus | 36 px | +100 PTS |
| Tier 5 (Drop) | 🟠 Persimmon | 🍩 Frosted Donut | 🌍 Earth | 45 px | +150 PTS |
| Tier 6 | 🍎 Red Apple | 🍮 Caramel Pudding | 🔵 Neptune | 55 px | +210 PTS |
| Tier 7 | 🍐 Asian Pear | 🍰 Strawberry Shortcake | ❄️ Uranus | 66 px | +280 PTS |
| Tier 8 | 🍑 Sweet Peach | 🍵 Matcha Roll Cake | 🪐 Saturn | 78 px | +360 PTS |
| Tier 9 | 🍍 Golden Pineapple | 🍫 Berry Tart Pie | ⚡ Jupiter | 91 px | +450 PTS |
| Tier 10 | 🍈 Melon Cantaloupe | 🥞 Soufflé Pancake Tower | 🌟 Sirius Blue Star | 106 px | +550 PTS |
| Tier 11 (MAX!) | 🍉 Giant Watermelon | 🎂 3-Tier Birthday Cake | ☀️ The Golden Sun | 124 px | +1,320 PTS! |