Bonding Cruve

The basis of a bonding curve for Bitboom

What is a Bonding Curve?

A bonding curve is a mathematical model that defines the relationship between the price and supply of a token. It establishes a structured mechanism for creating and trading tokens, allowing participants to buy and sell tokens at prices that adjust based on the total supply. This contrasts with traditional cryptocurrencies, where prices are often determined by market speculation.

How Does It Work Mathematically?

The bonding curve typically uses a predefined mathematical function that determines how the price of a token changes as more tokens are minted (created) or burned (destroyed). The most common forms of bonding curves include linear, exponential, and step functions.

Mathematical Representation

1. Basic Formula:

   • Let $PPP$ be the price of the token,

   • $SSS$ be the total supply of tokens,

   • $kkk$ be a constant that defines the steepness of the curve.

   A simple bonding curve can be represented as:

   $$P(S)=k⋅SnP(S) = k \cdot S^nP(S)=k⋅Sn$$

   where $nnn$ determines the type of curve:

   • $n=1n = 1n=1$: Linear

   • $n>1n > 1n>1$: Exponential

Bonding Curve

Illustration of Bonding Curve Dynamics in Bitboom

Token Launch Process:

• When a token is launched on Bitboom, let’s assume there are 800 million tokens available in the bonding curve.

• The total supply is capped at 1 billion tokens.

Sales and Market Dynamics:

• As users purchase tokens, the price per token increases according to the bonding curve.

• For example:

  • If the first 800 million tokens are sold, the price might increase in defined increments, say from $1 to $2, depending on the total market cap.

Market Cap Thresholds:

• Specific thresholds (like $69,000 for Bitcoin) trigger changes in the bonding curve.

• For instance, if the market cap hits $69,000, liquidity is injected into the market to stabilize prices and encourage trading.

Example Calculation

1. Initial Conditions:

   • Let’s say the bonding curve starts at a price of $1 for the first million tokens.

   • After selling 2 million tokens, the price could increment to $1.10.

2. Price Calculation:

   • If $S=2,000,000S = 2,000,000S=2,000,000$ and using a hypothetical equation:

   $$P(S)=1+0.1⋅(S1,000,000)P(S) = 1 + 0.1 \cdot \left(\frac{S}{1,000,000}\right)P(S)=1+0.1⋅(1,000,000S​)$$

   • For $S=2,000,000S = 2,000,000S=2,000,000$:

   $$P(2,000,000)=1+0.1⋅2=3P(2,000,000) = 1 + 0.1 \cdot 2 = 3P(2,000,000)=1+0.1⋅2=3$$

   • This price reflects the new value of the token based on the supply dynamics.