The Esher Droste Effect in Mantra VR creates an infinite spiral in your 360 Composition. This spiral can be keyframed in many ways and its parameters modified to create different effects. Charles Yeager goes through some of these effects in this tutorial video.
From SkyBox developers, Mantra VR is a 360/VR Stylization Plugin for After Effects and Premiere Pro.
Get a demo of Mantra VR: mettle.com/product/mantra-vr/