Mneme World Generator: System Architecture & Mechanics

Version: Draft 2.1 (Added Mutual Hill Radius Logic)

Philosophy: Simulationist, Recursive, Modular.

1. Core Design Philosophy

The core of the new design is a strictly defined hierarchy of physical and political objects. This structure allows for recursive code logic.

Example: A moon orbiting a planet uses the same physics engine class as a planet orbiting a star.

Goal: To model reality by breaking down stellar and civilization formation into procedural systems using RNGs to generate variety within scientific bounds.

2. The Hierarchy (Core Concepts)

The system is divided into four distinct levels of orbital magnitude and detail.

Level 1: Stellar & Barycenters (The Anchor)

Definition: The primary gravity well of the system.

Components: Stars, Companion Stars, and Barycenters (Centers of Mass).

Key Mechanics:

The "Rule of Five": Companion stars must be distant enough (typically >10 AU or very close <0.5 AU) to allow stable planetary orbits (Billion-year stability criteria).

Level 2: Inras (IntraStellar) Systems

Definition: The Major Orbitals orbiting the Level 1 Anchor.

Components: Gas Giants, Terrestrial Worlds, Dwarf Planets, Asteroid Belts, and Circumstellar Disks.

Key Mechanics:

Main World Habitability: Determining suitability for life based on Orbital Zone + Atmospheric Conditions.

Stellar Stability Equation: Used to calculate valid orbital slots.$$Stable Orbit = Gravity_{Pull} \rightleftharpoons (Luminosity_{Push} + Velocity_{Push})$$

Level 3: Sub-Systems

Definition: The Dependent Orbitals orbiting a Level 2 Body.

Components: Moons, Ring Systems, Co-orbitals (Trojans/Greeks), and Lagrange Point Clusters.

Key Mechanics:

Roche Limits: Determines if mass becomes a Ring System or consolidates into a Moon.

Tidal Locking: Effects of close proximity to the parent body (Rotation = Revolution).

Level 4: Details & Surface

Definition: Specific localities on or within a Level 3 or Level 2 Body.

Components:

Natural: Continents, Tectonic Regions, Craters, Biomes.

Artificial: Specific Habitats (O'Neill Cylinders), Surface-Based Centrifuges (called "Magicians") for low-G world adaptation.

3. Procedural Logic: The Star (Level 1)

The generation process begins at the top of the hierarchy. The characteristics of the Star define the "Budget" for the rest of the system.

A. Stellar Classification Generation (Primary)

Class Roll: 5D6 (Mneme PDF p.13)

Determines the Spectral Type (O, B, A, F, G, K, M).

Grade Roll: 5D6 (Mneme PDF p.13)

Determines the Size/Luminosity (Supergiant, Giant, Main Sequence, Dwarf).

Note: Higher Grade number (e.g., 9) = Lower Luminosity. Lower Grade number (e.g., 0) = Higher Luminosity.

B. Mass Determination & System Budget

The Star's mass acts as the seed for the complexity of the system.

System Mass Budget: The star's mass determines the available mass for the INRASS (Intrastellar Systems).

Advantage/Disadvantage Mechanic:

Massier stars may roll Advantage on the number of orbits but Disadvantage on stability.

C. The Stability Cut-Off

The Filter: There is a hard logic cut-off for high-mass/high-luminosity stars.

Constraint: If a star has too much Gravity and Stellar Radiance (e.g., O or B Class types), it prevents the formation of stable terrestrial worlds.

D. Companion Stars (Level 1 Sub-Systems)

Companion stars are generated recursively but are constrained by the Primary's gravity.

1. Existence Roll (The Companion Star Table)

Mechanic: Roll 2D6.

Target Number: Depends on the Primary Star's Class and Grade (See PDF p.14).

The "Multiple Star" Rule: If the result is a natural 12, a companion exists AND you roll again to check for a second companion (Trinary system). This repeats on subsequent 12s.

2. Companion Characteristics (The Multiplier Cap)

To ensure the Companion is never more massive or luminous than the Primary, the generation roll is capped using a multiplier derived from the Primary's stats.

Concept: Instead of re-rolling or forcing a value, the maximum possible result for the Companion is clamped to the Primary's current value.

The Logic:

Convert Primary's Class/Grade to a linear value (e.g., 0-100 scale).

Calculate a Cap Multiplier = Primary Value / Max Possible Value.

Roll for Companion normally.

Multiply the result by the Cap Multiplier.

Outcome: This mathematically guarantees the Companion is always $\le$ Primary without needing complex "If/Then" lookup tables.

3. Orbital Placement (The 3D6 Orbit Table)

Mechanic: Roll 3D6 to determine distance in AU.

Variable Distance: The result gives a range. The exact distance is randomized within that range.

Contact Binaries: If the distance is smaller than the star's physical radius, they are treated as Contact Stars.

4. Hierarchy of Orbits (Multi-Star Systems)

For systems with 3+ stars, we must determine the hierarchy.

Roll D6:

1-3: The new star orbits the Primary (P-Type / Circumbinary potential).

4-6: The new star orbits the Previous Companion (S-Type / Hierarchical).

5. The "Rule of Five" (Orbital Stability)

This rule defines the "Forbidden Zones" where planets cannot exist due to gravitational interference.

Inner Limit: Distance / 5

Outer Limit: Distance * 5

Constraint: No stable planetary orbits can be generated between these two values.

4. Determine Main World (Prime Inras)

Before the full system is populated, the Main World (Prime Inras)—the primary point of interest—is generated. This ensures every system has a focal point for gameplay.

A. Determine Main World Type

Mechanic: Roll 2D6 on World Type Table A (PDF p.19).

Outcomes:

Habitat (Artificial): System has no habitable planet. Population lives in space habitats (measured in Mega/Giga Volume Tons).

Dwarf Planet: Main world is small (measured in Lunar Masses). Type determined by 2D6 roll (Carbonaceous, Silicaceous, Metallic).

Terrestrial World: Standard rocky planet (measured in Earth Masses).

Modifiers:

F-Class Stars: Adv+2 to Size roll.

G-Class Stars: Adv+1 to Size roll.

B. Determine Habitability (Waterfall Algorithm)

Instead of a complex lookup table, Habitability is determined by a Waterfall Algorithm where each step modifies the probabilities of the next.

Step 1: Mass & Gravity

Roll: Determines the world's ability to retain an atmosphere.

Logic: Low mass worlds apply Disadvantage to Step 5 (Atmosphere). High mass worlds apply Advantage.

Step 2: Orbital Position (Zone)

Roll: Determines the raw solar flux (energy received).

Logic:

Inner Zone: Applies Advantage to Step 6 (Temperature) but Disadvantage to Step 3 (Biochem/Water) due to evaporation.

Outer Zone: Applies Disadvantage to Step 6 (Temperature) but Advantage to Step 3 (Biochem/Volatiles) due to ice retention.

Step 3: Composition (Biochem/Resources)

Roll: Determines the presence of volatiles (Water, Ammonia, Methane) and minerals.

Logic: If Volatiles are absent (Desert World), Step 5 (Atmosphere) is capped. If abundant, Step 5 gains modifiers toward "Dense".

Step 4: Hazards (The Filter)

Roll: Checks for system-specific threats (Flare Star, Radiation Belt, Toxic Primordial Soup).

Logic: High hazards can immediately disqualify the world from being "Garden" class.

Step 5: Atmosphere

Roll: Determined by Mass (Step 1) + Volatiles (Step 3).

Logic: Generates pressure (Vacuum to Crushing). Acts as a Multiplier for Temperature (Greenhouse Effect).

Step 6: Temperature (Final State)

Roll: Calculated from Position (Step 2) modified by Atmosphere (Step 5).

Result: This final state determines the Habitability Rating.

C. Determine Inhabitants

World Development (HDI Roll):

Mechanic: Roll 2D6 (Mneme PDF p.27).

Result: Determines HDI (Underdeveloped to Very Developed) and World Average SOC.

Inequality Roll (Gini Coefficient):

Roll: Determines Inequality Rating (Low to Extreme).

The Elite Ratio (Formula):$$Elite Ratio = \frac{1}{(Gini Score + 1)} \times 10\%$$

Effective Standard of Living:

Formula:$$Effective SOC = Individual SOC + (World Average SOC - 7)$$

Access Logic (The Tech Divide):

High SOC (Elites): Full access to Setting TL.

Mid SOC (Citizens): Access to Standard TL.

Low SOC (Subsistence): Restricted to Scavenged/Archaic Tech.

D. Determine Starport

Mechanic: Starport quality is derived from the World's Population, Tech Level, and Wealth.

PVS (Port Value Score): A calculated metric (Habitability/4 + TL-7 + Wealth Modifiers) determining the port's capabilities (A, B, C, D, E, X).

5. Determine Planetary Systems (Inras Roll)

Once the Level 1 Anchor and Prime Inras are defined, the rest of the system is populated.

A. The Inras Roll (Quantity & Type)

Mechanic: A roll is made for each category of celestial object to determine how many exist in the system. The result can be zero.

Categories:

Disks: Circumstellar/Proto-planetary disks.

Dwarves: Dwarf Planets (Ceres-like).

Terrestrials: Rocky worlds (Mars/Earth/Venus-like).

Ice: Ice Giants (Neptune/Uranus-like).

Gas: Gas Giants (Jupiter/Saturn-like).

B. Mass Determination

Base Roll: For each object generated, roll 2D6 to determine its base mass category.

Precise Mass (Optional/Software): Roll D66.

Calculation: Base Mass x (D66 Result Multiplier) to get a precise, varied mass (e.g., 1.4 Earth Masses vs. just "1 Earth Mass").

6. Determine Planetary Positions (Waterfall Placement)

Planetary positions are determined by Gravitational Dominance and Hill Stability.

A. The Waterfall Technique

Principle: Massive objects settle into stable orbits first. Smaller objects are forced into remaining slots or captured.

Process:

Sort all generated objects by Mass (Highest to Lowest).

Place Object 1 (Highest Mass): Determine ideal position (e.g., Gas Giant at Snow Line).

Calculate Forbidden Zone: Using the Mutual Hill Radius ($R_H$) formula. $$R_H = \left(\frac{a_1 + a_2}{2}\right) \sqrt[3]{\frac{m_1 + m_2}{3 M_{Star}}}$$

Place Object 2: Must be at distance $\Delta a > K \cdot R_H$ where K=5 (Mneme Stability Standard).

Repeat: Until all objects are placed. Objects that cannot fit are ejected or captured as moons.

Appendix A: New Concepts

The Doubling Power Scale (Base-2)

Mneme retools the traditional Cepheus Engine SOC (Social Standing) statistic to reflect Power-Law Distributions.

The Scale: Social Standing operates on a Base-2 Logarithmic Scale (Doubling).

The Mechanic: Every +1 SOC represents a 2x increase in Income (MC - Mneme Credits), Wealth, and Resource Access.

Rounding: For calculation ease, doubling 4 results in 5 (or a similar adjustment to keep numbers clean in the tens/hundreds).

Perspective:

SOC 10-11: "Billionaire" / Head of State (High SOC, but common in an 80B population).

SOC 14+: Stellar Elite (Owns Habitats/Megacorps).

Technology as GDP Multiplier

Concept: Higher Tech = Higher Productivity.

Outcome: A SOC 3 person on a TL 15 world may have a higher material standard of living than a SOC 12 person on a TL 3 world.

Appendix B: Equipment & Assets

Vacc Suits & Environmental Gear

Visuals: The Vacc Suit Table will be updated with detailed art and examples.

Procedural Generation: Justin and Nicco will create a Blender File using Procedural Geometry Nodes.

Function: Allows for random, procedurally generated Vacc Suit designs (visuals) based on Tech Level and Type.

Modifiers:

Hazmat Suits: Small negative modifiers to DEX/Mobility.

HE (Hostile Environment) Suits: Higher negative modifiers due to bulk/armor.

Mneme Placement Logic: The Gravitational Waterfall

Objective: To place planets in a system based on "Mass Dominance" (Heaviest First) rather than random slotting.

Algorithm Type: Insertion Sort with Physics Constraints (Hill Stability).

1. The Core Variable: Mutual Hill Radius ($R_H$)

To determine if two planets can exist near each other without colliding or ejecting one another, we use the Mutual Hill Radius. This defines the "gravitational reach" of two planets relative to the star they orbit.

The Formula

$$R_H = \left( \frac{a_1 + a_2}{2} \right) \sqrt[3]{\frac{m_1 + m_2}{3 M_{Star}}}$$

Variable Definitions (Deep Dive)

1. $a$ = Semi-Major Axis (Orbital Distance)

Definition: The "average" distance of a planet from its star.

In Detail: Orbits are rarely perfect circles; they are ellipses (ovals).

The Major Axis is the longest line that can be drawn through the center of the oval.

The Semi-Major Axis ($a$) is exactly half of that line (like the radius of a circle, but for the longest part of the oval).

Why we use it: It is the standard metric for defining the size of an orbit. In our code, a is measured in Astronomical Units (AU), where 1.0 AU is the distance from Earth to the Sun.

In the Formula: $\frac{a_1 + a_2}{2}$ calculates the average distance from the star to the gap between the two planets.

2. $m$ = Planet Mass

Definition: The mass of the planets involved.

Unit: Must be consistent (e.g., Earth Masses or kg).

Impact: Heavier planets have larger Hill Radii. A Gas Giant clears a massive path; a Dwarf Planet clears a tiny one.

3. $M_{Star}$ = Star Mass

Definition: The mass of the central star.

Impact: The star acts as the "dominator." A massive star (high gravity) compresses the Hill Radii of its planets, allowing them to orbit closer together. A weak star (Red Dwarf) has a looser grip, so planets effectively have "wider" gravitational spheres relative to the star, forcing them to be spaced further apart.

2. The Jupiter-Saturn Baseline (The Proof)

This baseline establishes why we use $K=5$ as our safety multiplier.

Jupiter (5.2 AU) & Saturn (9.5 AU): Separation is ~4.3 AU.

Stability Calculation: They are separated by approximately 8 Mutual Hill Radii.

The Mneme Standard:

Chaos Limit: $K < 3.5$ (Unstable).

Mneme "Forbidden Zone": $K < 5$ (The "Rule of Five").

Relaxed System: $K \approx 8$ (Sol-like).

3. Calculating the Orbital Zones

Before any planets are placed, the "Map" of the system is drawn based on the Star's Luminosity ($L_{Star}$).

A. The Snow Line ($D_{snow}$)

The critical boundary where volatiles (water, ammonia) freeze. This is the seed point for Gas Giant formation.

Formula: $$ D_{snow} = 2.7 \times \sqrt{L_{Star}}

B. The Habitable Zone ($HZ$)

The Goldilocks zone where liquid water can exist.

Center of HZ: $$ HZ_{center} = \sqrt{L_{Star}}

Inner Edge: $$ HZ_{in} = 0.95 \times HZ_{center}

Outer Edge: $$ HZ_{out} = 1.37 \times HZ_{center}

C. The Zone Map

Infernal Zone: 0.0 to $0.1$ AU (Hot Jupiters).

Inner Zone: $0.1$ AU to $HZ_{in}$.

Habitable Zone: $HZ_{in}$ to $HZ_{out}$.

Outer Zone: $HZ_{out}$ to $D_{snow}$ (The Asteroid Belt usually forms here).

Frozen Zone (Giants): $D_{snow}$ to $100$ AU.

Scatter Disk (Far Outer): $> 100$ AU.

4. The Process: "The Gravitational Queue"

Think of the orbital lines as a queue. When a new, heavy person (Planet) arrives, they decide where they want to stand. If they force themselves into the front or middle of the line, everyone behind them must take a step back.

Pre-Requisite: Sort the Object Pool by Mass (Descending). Place the heaviest objects first.

Step 1: The Placement Roll (The Intent)

This step determines where the planet wants to go.

A. Gas & Ice Giants (Migration Logic)

Giants form beyond the Snow Line but can migrate.

Placement Roll: Roll 2D6.

Standard Placement (Type I-III): $$a_{target} = D_{snow} + \left( D_{snow} \times \frac{Roll}{6} \right)$$

Result: Giants naturally form at $1.3x$ to $3.0x$ the Snow Line distance.

Exploding Dice (Outer Migration):

Trigger: If Roll = 12.

Effect: Roll 2D6 again. Multiply the final distance. Repeat if 12 is rolled again.

Inner Migration (The 1% Chance):

Trigger: If Roll = 2.

Check: Roll 2D6. If $< 8$, become Hot Jupiter ($0.05 - 0.1$ AU).

B. Terrestrial & Dwarf Worlds (The Overflow Rule)

Terrestrial placement depends on how crowded the inner system is.

Check Crowd Status (The Gap Analysis): Instead of counting planets, we mathematically check if the "Inner System" (Inner + Habitable Zones) has any Gravitational Real Estate remaining.

Identify Gaps: Sort all current planets in the Inner/Habitable range.

Calculate Required Space ($W_{req}$): For the new planet ($P_{new}$), calculate the space it needs to be stable against a theoretical neighbor:

$$W_{req} \approx 10 \times R_H(P_{new}, P_{average})$$

Check Gaps: Scan every gap between existing planets (and the star/zone edges).

If Gap Width > $W_{req}$: The System is OPEN. (New planet can squeeze in).

If Gap Width < $W_{req}$ for ALL gaps: The System is FULL.

State A: Open System (Not Full)

Roll: 2D6.

Target: Fair odds for any zone.

2-4: Inner Zone (Hot/Infernal).

5-9: Habitable Zone (Goldilocks).

10-12: Outer Zone (Cold).

State B: Crowded System (Full)

Rule: If the Inner System is full, the planet is forced outward.

Roll: 2D6 determines "Degrees of Outer".

2-6: Just beyond the last Inner Planet (Outer Zone).

7-10: Frozen Zone (near Snow Line).

11-12: Scatter Disk (Far Outer).

Step 2: The Insertion Check (The Scan)

Look at the planets already placed on the map. Find where $a_{target}$ sits relative to them.

Scenario A (The Empty Slot): The target spot is far away from everyone.

Action: Place immediately. No adjustments needed.

Scenario B (The Conflict): The target spot is inside the Forbidden Zone ($K < 5$) of an existing planet.

Action: Trigger The Shove.

Step 3: The Shove (Hill Radius Modification)

The Shove Logic:

If $P_{new}$ forces itself into $a_{new}$, we must check the next planet out ($P_{outer}$).

Calculate: Mutual Hill Radius ($R_H$) between $P_{new}$ and $P_{outer}$.

Calculate: Minimum Safe Distance ($D_{safe} = 5 \times R_H$).

The Test: Is $(a_{outer} - a_{new}) < D_{safe}$?

The Adjustment: $$a_{outer\_new} = a_{new} + (5 \times R_H) + \text{Variance}$$ Translation: Pick up the outer planet and move it to exactly the edge of the safety zone.

The "Far Outer" Exception:

If $P_{outer}$ is already in the Scatter Disk (>100 AU), it is not moved.

Instead, $P_{new}$ (the intruder) is forced to find a different slot or is ejected. This protects the distant Oort Cloud/Scatter objects from being shuffled by inner system dynamics.

Step 4: The Ripple Effect (The Chain Reaction)

If you moved $P_{outer}$ in Step 3, that planet might now be too close to its outer neighbor. You must repeat the check down the line.

Did moving Planet 2 bump into Planet 3?

Yes: Move Planet 3 outward using the same Shove formula relative to Planet 2's new position.

No: Stop. The ripple has faded.

5. Procedural Example: "The Overflow"

Current System State:

Planet 1: Gas Giant at 3.0 AU (Snow Line).

Planet 2: Terrestrial at 1.0 AU (Habitable).

Planet 3: Terrestrial at 0.7 AU (Inner).

New Arrival:

Planet 4: A new Terrestrial World.

Logic:

Crowd Check: Inner system has 2 planets. Is it full? Let's say Limit = 2. YES, FULL.

The Overflow Rule: Planet 4 cannot roll for Inner/Habitable. It MUST roll on the Crowded Table.

The Roll: Rolls an 8 (Frozen Zone).

Placement: Target becomes ~3.5 AU (Just outside the Gas Giant).

Shove Check: It conflicts with the Gas Giant (3.0 AU).

Resolution: Planet 4 is "light", Gas Giant is "heavy". The Gas Giant stays. Planet 4 is pushed further out to 3.8 AU.