This ShaderToy shows the stable region of a nonlinear periodic system (analogous to some accelerators).   Like the Mandelbrot set, black indicates stability and colours show how long unstable particles take to escape.   By dragging the mouse horizontally you can change the "phase advance" before each nonlinear kick and observe patterns of 6,5,4,3 "islands" appearing when this advance is near 1/6, 1/5, 1/4, 1/3.    #physics #accelerators #dynamics 
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<br /><a href='https://www.shadertoy.com/view/7XVGDz'>https://www.shadertoy.com/view/7XVGDz</a><p><a href='posts/202609/post-20260924-171744-a.png'><img src='posts/202609/post-20260924-171744-a.png' loading='lazy' /></a></p>