MikeTateMath.org

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Mike Tate Mathematics

RPG Toolkit

๐Ÿ”ข Numeric Codex โ€” Aurora Forge

Output: โ€”
Level 1 Quick Start โ–ธ

What it does: Enter a comma-separated list (e.g., 2, 4, 8, 16) and choose a transform (ร—2, square, index-scale). Each value becomes a colored bar; the connecting line shows the overall shape.

How to read it: Taller bars mean larger values. If the line keeps a steady slope across a transform, your list scales proportionally; sharp bends highlight imbalance or outliers.

Level 2 Mechanics โ–ธ

Transforms:

  • ร—2 โ†’ n โ†ฆ 2n (uniform scaling)
  • square โ†’ n โ†ฆ nยฒ (magnifies differences)
  • index-scale โ†’ n โ†ฆ nยท(i+1) (weights by position)

Animation: values ease toward targets using current += 0.12 ยท (target โˆ’ current) for smooth transitions. The canvas is device-pixel-ratio aware for crisp edges and grid lines.

Level 3 Pattern & Design Notes โ–ธ

Interpreting shape: If ร—2 preserves the silhouette but square pushes the tail upward, your data is closer to linear than quadratic growth.

Tuning ideas: Adjust the easing constant to change transition speed; add a midline to visualize negatives; use a line-only mode for large lists to emphasize curvature over amplitude.

๐Ÿ”ฃ Symbol Resonator โ€” Glyph-Wave

Resonance: โ€”
Tier 1 Concept โ€” Encoded Motion โ–ธ

Type any symbols; the Resonator turns each character into a point on a shared waveform. Letters, digits, runesโ€”every mark contributes to a continuous line you can see breathing on the canvas. One stream, many signs.

Tier 2 Structure โ€” Transformation Modes โ–ธ

raw maps code points directly; wrap folds values into a bounded band; sine projects values into a harmonic curve; pulse adds timed amplitude wobble. Modes re-shape the same content without breaking continuity.

Tier 3 Deep Pattern โ€” Resonant Topology โ–ธ

Stable phrases settle into smooth loops; mixed alphabets create phase shifts and beats. What youโ€™re seeing is the textโ€™s structure expressed as motionโ€”repetition, inversion, and returnโ€”so you can read with your eyes what you wrote with symbols.

RPG Dice Lab

d

Enter NdM + K. The numbers swirl like sigils; the total glows in gold.

โšก Arc Notes

Level 1 Quick Primer โ–ธ

What youโ€™re seeing. The neon ridge and bars summarize the likelihood landscape of your current dice recipe. Peaks mark the most common totals; valleys mark rarities. The soft glow strengthens where outcomes stack upโ€”so a bright ridge means โ€œexpect this often.โ€

  • Line height โ‰ˆ relative frequency for that total.
  • Glow = recent confirmations; it fades over time.
  • Shallow slope โ‡’ broad spread; sharp spike โ‡’ narrow, predictable results.
Level 2 Field Lines โ–ธ

How the ridge is drawn. We estimate a smoothed distribution and then let recent rolls โ€œchargeโ€ it:

  1. Sampling. Simulate many trials of NdM + K to build a histogram.
  2. Smoothing. Blur with a small kernel (or EMA) so bars merge into a continuous ridge.
  3. Threshold. Emit glow where density crosses a floor to suppress noise tails.
  4. Decay. Each real roll adds energy to its bin; energy decays by e-t/ฯ„ so the glow โ€œforgets.โ€

Knobs: trials (resolution), kernel width (sharpโ†”soft), threshold (clarity), decay time ฯ„ (memory).

Level 3 Discharge Model โ–ธ

Why it behaves like lightning. Treat each total x as a node with charge Qx. A roll at x injects ฮ”Q; between rolls the system discharges:

dQx/dt = -Qx/ฯ„ + ฮฃhits at x ฮ”Q

  • Peaks are stable attractors for symmetric dice (bell near n(m+1)/2 + k).
  • Stability windows. Small ฯ„ tracks moment-to-moment luck; large ฯ„ shows the long-run law.
  • Chaos zones. Advantage/disadvantage or extra dice shift, split, or flatten massโ€”explaining why +1d4 nudges while Adv reshapes.

Design note: The meter communicates both theory (expected shape) and history (charged glow) without numbersโ€”players feel the math first.

๐Ÿ’ฐ Weighted Loot Roller

Weights are relative: higher weight โ‡’ more likely. Emojis auto-detect from the name.
Item Rarity Weight Wins
0
0
0
0
โ€”

โ„ Frost Ledger โ€” Roller Guide

Level 1 Quick Use โ–ธ
  1. Edit items: type a name; the emoji chip updates automatically from keywords.
  2. Pick rarity: click the pill to cycle Common โ†’ Uncommon โ†’ Rare โ†’ Epic โ†’ Legendary.
  3. Set weight: bigger number โ‡’ more likely (weights are relative, not %).
  4. Roll: use Roll ร—1 or Roll ร—10. A floating card announces hits; the summary line lists totals.
  5. Utilities: Shuffle Weights nudges all weights ยฑ30%. Clear Counts resets the Wins column.
Level 2 Odds & FX โ–ธ
  • Relative odds: Chance(item i) = wแตข / ฮฃ w.
  • Rarity styling: rarity controls halo/scale; Rare twinkles, Legendary gets a gold sweep.
  • Emoji mapping: names like โ€œswordโ€, โ€œgemโ€, โ€œpotionโ€, โ€œringโ€, โ€œmaskโ€, โ€œfanโ€ map to themed emojis; otherwise rarity fallback.
  • Wins counter: increments per hit to reveal bias during test runs.
  • Perf: CSS animations + tiny DOM; sparks auto-cleanup โ‰ˆ900ms.
Level 3 Balancing Notes โ–ธ
  • Start with ratios: e.g., 60:25:10:5; test with ร—10 rolls and trim ยฑ10%.
  • Readability: keep names short; let emoji + rarity scan first.
  • Demo tuning: if Legendaries feel too rare for demos, temporarily double their weight.
  • Extend: add rows freelyโ€”picker recalculates without extra wiring.

๐ŸŽฒ D20 Quick Roller โ€” The Orb of Fate

Last: โ€”
Recent:

    โˆž Mรถbius Insight โ€” D20 Orb Guide

    Tier 1 Single Surface Idea โ–ธ
    1. Set DC (target) and Modifier (your bonus).
    2. Pick Mode: Normal, Advantage, Disadvantage, or with +1d4.
    3. Roll via the button or by tapping the orb. โ€œLastโ€ and the chips update.
    4. Formula: (d20 โŸ‚ mode) + modifier (+ d4) vs DC.
    Tier 2 Twist & Continuity โ–ธ
    • Adv/Dis: roll 2d20; Adv keeps higher, Dis keeps lower.
    • +1d4: adds 1โ€“4 after the d20 and modifier.
    • Success: (d20 ยฑ mode) + mod + (opt d4) โ‰ฅ DC.
    • Chips: green = success, sepia = fail; โ€œLastโ€ mirrors the orb.
    • Canvas: DPR-scaled; rings/glow add depth without images.
    Tier 3 Topology Take โ–ธ
    • Hit chance (Normal): need d20 โ‰ฅ DC โˆ’ mod. โ‰ˆ max(0,min(1,(21 โˆ’ (DC โˆ’ mod))/20)).
    • Adv: success โ‰ˆ 1 โˆ’ (1 โˆ’ p)ยฒ (boosts mid DCs).
    • Dis: success โ‰ˆ pยฒ (punishes mid DCs).
    • +1d4: bumps marginal cases by ~1โ€“3.
    • DC tuning: โ€œtense but fairโ€ โ‰ˆ 8 + partyโ€™s typical mod (Normal).

    Mรถbius cue: small twists (Adv/Dis, +1d4) change the path on the same probability surface.

    Tap the orb to challenge probability itself.

    โ›ฉ๏ธ Loot Shrine

    Pray to Probability
    At this shrine, math answers with miracles โ€” if your stats are worthy.
    Tier 1 Quick Use โ–ธ

    Roll ร—1 does a single pull. Roll ร—10 runs a batch.

    Each result rises as a glowing card; the chip on the right logs your last pull.

    The Loot Table lists every item with its rarity.

    Tier 2 Under the Hood โ–ธ
    • Weighted randomness: bigger weight โ‡’ higher chance.
    • Blessing can upgrade a drop one tier (Common โ†’ โ€ฆ โ†’ Legendary).
    • Rarity sets card size, border glow, and special FX (coins for Legendaries).
    Tier 3 Balancing & Odds โ–ธ
    • Relative odds: doubling an itemโ€™s weight doubles its chance vs. peers.
    • Blessing cap: ~35%, nudged by Focus/Crit passives.
    • Counts persist locally until you hit Clear Counts or reload.

    All RNG is client-sideโ€”no server calls.

    RarityItem
    โ€”

    Modular Harmonic Visualizer

    โš™๏ธ Simulation & Visualization Suite

    โš›๏ธ Harmonic Codex Suite

    Access the living resonance of your experimental toolkit.

    ๐ŸŽฒ Dice Lab ๐Ÿ”ข Numeric Codex ๐Ÿ”ฃ Symbol Resonator ๐Ÿ’Ž Loot Roller