LORE Token Bonding Curve

This project demonstrates a token sale mechanism using a polynomial bonding curve for automatic price discovery.

Components

1. Bonding Curve Visualization Script: A Python script that generates visualizations of token price curves with different exponents.
2. Interactive Web App: A Next.js application that allows users to simulate buying and selling tokens on the bonding curve.

Bonding Curve Mechanics

The bonding curve uses a polynomial formula (x^n) where:

• n is the exponent parameter (typically between 1 and 3)
• The price of tokens increases as more tokens are purchased (convex curve)
• The price decreases as tokens are sold back to the contract

Getting Started

Visualization Script

To generate the bonding curve visualization:

1. Set up a Python virtual environment:

   python3 -m venv venv
   source venv/bin/activate
   pip install -r requirements.txt

2. Run the visualization script:

   python scripts/bonding_curve_visualization.py

This will generate a bonding_curve.png file showing different curves with various exponents.

Web App

The web app provides an interactive simulation of the bonding curve:

1. Navigate to the app directory:

   cd app

2. Install dependencies:

   npm install

3. Run the development server:

   npm run dev

4. Visit http://localhost:3000 in your browser and click on "Try Bonding Curve Simulator"

Features

• Curve Visualization: Interactive chart showing the bonding curve with adjustable exponents
• Buy/Sell Simulation: Test how buying and selling affects price and token supply
• Price Calculations: See how different transaction amounts impact price slippage
• Wallet Simulation: Track your simulated token and ETH balances

How It Works

1. Buying Tokens:

   • User sends ETH to buy tokens
   • Price is calculated based on the current supply and exponent
   • Tokens are added to the user's balance
   • Supply increases

2. Selling Tokens:

   • User sells tokens back to the contract
   • Price is calculated based on the new (reduced) supply
   • ETH is added to the user's balance
   • Supply decreases

Formulas

• Token Price: price = (supply / max_supply)^n * max_price
• Buy Return (simplified): tokens = eth_amount / current_price
• Sell Return (simplified): eth = token_amount * current_price

In a production implementation, integral calculus would be used to accurately calculate the area under the curve for precise token/ETH amounts.