# Graphdle

> Graphdle is The Daily Graph Transformation Puzzle.

Graphdle is a browser-based mathematical puzzle game where players compare two function graphs and reconstruct the hidden chain of graph transformations that turns the base graph into the target graph. Players can compare results on global leaderboards or create private leagues to compete with friends.

## Site

- URL: https://graphdle.com/
- Sitemap: https://graphdle.com/sitemap.xml
- Robots: https://graphdle.com/robots.txt

## What Players Do

Players are shown a base function graph, usually called f(x), and a target graph. They submit a chain of transformations such as `shift(2)`, `vshift(-1)`, `derivative`, `integral`, `floor`, `abs`, `convolve(1)`, or nested expressions like `derivative(shift(2))`.

The goal is to match the hidden transformation chain within a limited number of attempts.

## Modes

- Daily: one shared daily puzzle per difficulty.
- Random: repeatable practice with random puzzles.
- Tutorial: guided lessons for individual transformation types.
- Private leagues: groups can compare daily scores.

## Difficulty

- Easy: visual graph transformations such as shifts, scaling, reflections, and absolute value.
- Normal: calculus, clipping, rounding, and simple nonlinear transforms.
- Hard: second derivatives, logarithmic and exponential transforms, smoothing, noise, and advanced distortions.

## Input Syntax

Graphdle supports a compact DSL for graph transformations. Operators are nested with the outermost operation written first. For example:

- `shift(2)`: evaluate f(x - 2), shifting the graph right.
- `vshift(1)`: add 1 to the output.
- `vscale(2)`: multiply y-values by 2.
- `scale(2)`: evaluate f(2*x), compressing horizontally.
- `reflectX`: multiply output by -1.
- `reflectY`: evaluate f(-x).
- `derivative(shift(2))`: shift first, then differentiate.

Graphdle also has an ASCII-safe math transform resolver for supported transform notation using `f(x)`, such as `y = d/dx(int(floor(f(x))) dx)`, which maps back to the DSL.

## Suggested Summary

Graphdle is The Daily Graph Transformation Puzzle: a maths puzzle where players infer the chain of function transformations that maps one graph to another.