Bonding curves, simply

Temiloluwa — Sat, 03 Aug 2024 02:53:40 +0000

At first glance, bonding curves sound like some sort of fancy term for another abstract thing in computation, but bonding curves turn out to be a quite interesting thing in finance and mathematics.

Bonding curves simply put, are a mathematical formula for the calculation of an asset's value, in relation to the supply of the said asset.

Bonding curves are another mathematical model for asset valuation and pricing, in proportion to the asset supply and liquidity available for such assets. For better illustration, think of it as a line (or curve) on a graph that shows how the price of a token changes as more tokens are created or sold.

Say we have a token (LCD), and we want to use a bonding curve to determine the value of 1 LCD, we can derive the price using the mathematical formula being used in the specific bonding curve.

There are mainly two types of bonding curves;

Linear Bonding Curves
Exponential bonding curves

Linear Bonding Curves

A linear bonding curve increases the price of an asset in a straight line as more units of the assets are created. This means the price increases at a constant rate for each additional asset, or the asset price is directly proportional to asset supply (P∝S).

The formula for a linear bonding curve is:

P = m⋅S+b
where;

P = price of the asset
m = slope of the curve (rate of price increase per asset)
S = asset supply (number of existing assets)
b = initial price (when supply = 0)

A sample graph showing a linear bonding curve. The straight slope shows a direct proportion of asset price to asset supply

How it Works

Initial Price (b): This is the starting price of the asset when no assets have been issued yet.
Slope (m): This determines how much the price increases with each new asset issued.
Supply (S): As more assets are issued, the supply increases, and the price is recalculated.

Example:

Initial price (b) = $1
Slope (m) = $0.10 per asset

When no assets are issued:
P=0.10⋅0+1=1

When 1 asset is issued:
P=0.10⋅1+1=1.10

When 2 assets are issued:
P=0.10⋅2+1=1.20

Exponential Bonding Curves

An exponential bonding curve increases the price of an asset exponentially as more assets are issued. This means the price starts low but increases rapidly with each additional asset, or the asset value is exponentially proportional to the asset supply (P∝e^S)

The formula for an exponential bonding curve is:

P = a⋅e^(b⋅S)
where:

P: Price of the asset
S: Supply of the asset (number of existing assets)
a: Initial price (starting multiplier)
b: Exponential growth rate

A sample graph showing an exponential bonding curve. The slope advances slowly, and then increases sharply, showing an exponential increase with further supply addition.

How it Works

Initial Price (a): This is the starting multiplier for the price.
Exponential Growth Rate (b): This determines how quickly the price increases as more tokens are issued.
Supply (S): As more tokens are issued, the supply increases, and the price is recalculated using the exponential formula.

Example:
Initial price (a) = $1
Growth rate (b) = 0.1

When no tokens are issued:
P=1⋅e^(0.1⋅0) =1
When 1 token is issued:
P=1⋅e^(0.1⋅1) ≈ 1.105
When 2 tokens are issued:
P=1⋅e^(0.1⋅2) ≈ 1.221

Conclusion

Bonding curves provide a systematic way to manage the price and supply of assets. They ensure that early buyers are rewarded and that the asset price reflects demand.

Bonding curves can be applied to DeFi, and used to reward early participants of token sales, or to maintain the price of decentralised assets while reflecting the demand. By understanding these curves, projects can create sustainable and fair economic models for their tokens.

Deploying a PHP app to cPanel

Temiloluwa — Wed, 13 Jan 2021 22:16:02 +0000

Deploying a PHP web-app can be stressful for beginners who are using cPanel hosting for the first time, or who aren't conversant with the interface. Most issues encountered would be related to improper uploads, server name issues, or database errors.

What is cPanel

cPanel is a web hosting control panel that provides a graphical interface and automation tools designed to simplify the process of hosting a web site to the website owner or the "end-user".
cPanel can be used to host various software, including WordPress, Python Apps, PHP apps, Node.js apps, etc.

Deploying to cPanel

The cPanel interface

This is the default cPanel interface, customizable to user's taste.

Locate the File Manager

Find the public_html folder

Locate the Upload button

Upload a zipped folder of all the site files

Back to the file manager, and extract the files.

Replace all necessary information, such as server name, username, and password, for connecting to your database

With this, your PHP app should be visible at the domain (https://website.com)

You could reach out to me on Twitter if you encounter any issues along the way

DEV Community: Temiloluwa

Bonding curves, simply

Linear Bonding Curves

How it Works

Exponential Bonding Curves

How it Works

Conclusion

Deploying a PHP app to cPanel

What is cPanel

Deploying to cPanel

The cPanel interface

Locate the File Manager

Find the public_html folder

Locate the Upload button

Upload a zipped folder of all the site files

Back to the file manager, and extract the files.

Replace all necessary information, such as server name, username, and password, for connecting to your database