# Attractor Basin / 吸引子盆地

Visualization of basins of attraction for multiple attractors on the complex plane

> Canonical page: https://elysiatools.com/en/visualizations/attractor-basin

- **Category:** Math

## Overview

Comprehensive attractor basin visualization showing convergence domains for multiple dynamical systems on the complex plane. Features two system types: (1) Newton Fractals - Five polynomial presets including z^3-1 (3 roots), z^4-1 (4 roots), z^5-1 (5 roots), z^6-1 (6 roots), and z^3-2z+2 (custom roots) using Newton's iteration z_{n+1} = z_n - f(z_n)/f'(z_n). (2) Quadratic Maps - Three complex parameter values exploring Julia set dynamics: c = -0.7+0.3i, c = -0.8+0.156i (period-3), and c = -0.4+0.6i, using iteration z_{n+1} = z_n^2 + c. Three coloring modes: by basin (attractor identity), by iterations (convergence speed), and smooth coloring (gradient interpolation). Five color schemes: rainbow, pastel, neon, thermal, ocean. Adjustable parameters: max iterations (20-500), convergence tolerance, quality presets. Interactive features: zoom with mouse wheel, pan by dragging, trace mode showing convergence trajectories from clicked points, attractor highlighting, and animation. Real-time displays: cursor position, convergence target, render time, and trace information (start point, final attractor, iterations used). Educational content covers historical background (Poincaré, Mandelbrot, Feigenbaum), mathematical principles of basins of attraction, fractal boundary properties, system comparisons (Newton vs quadratic dynamics), applications in numerical analysis, physics, biology, engineering, and art, exploration tips, and comprehensive control guide. Multi-language support (zh, en, es, fr, de, ru, pt).

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