Mandelbrot Set Visualizer

A desktop application for rendering and exploring the Mandelbrot set, built with C# and Avalonia UI targeting .NET 9.

About

The Mandelbrot set is one of the most famous fractals in mathematics. A point $c$ in the complex plane belongs to the set if the sequence defined by:

$$z_{n+1} = z_n^2 + c, \quad z_0 = 0$$

remains bounded (does not diverge to infinity). This application renders the set on a 1000×1000 pixel canvas, coloring points that belong to the set in red.

Features

• Real-time rendering of the Mandelbrot set
• Pan navigation using arrow keys to explore different regions
• Zoom in by pressing Space to increase magnification
• Adaptive iteration count — the maximum number of iterations automatically increases as you zoom deeper, improving detail at higher magnifications

Controls

Key	Action
Arrow Up	Pan up
Arrow Down	Pan down
Arrow Left	Pan left
Arrow Right	Pan right
Space	Zoom in

Performance Note

You can scroll (zoom) into the set to explore its infinitely complex boundary, but be aware that performance degrades significantly after a few zoom levels. The rendering is not heavily optimized — each zoom step requires recalculating every pixel on the canvas, and as the iteration count increases with deeper zoom levels, the computation becomes substantially more expensive. This is a known limitation of the current implementation and would require significant optimization (e.g., multithreading, GPU acceleration, or perturbation theory) to handle deep zooms smoothly.

Getting Started

Prerequisites

• .NET 9 SDK

Run

cd MandelBrot/MandelbrotApp
dotnet run

Tech Stack

• C# / .NET 9
• Avalonia UI 11.3 — cross-platform UI framework
• WriteableBitmap — pixel-level rendering