[b]Appolonius' Tangency Problem:[/b] [i]To draw a circle which is tangent to three given circles.[/i] D, D2, D3 each seek the nearest tangent point according to a simple differential model: [url]http://www.geogebratube.org/material/show/id/34821[/url]
If seek is on, -EATING should always hunt for the circle which encloses the given three. -{drinking} should hunt for the circle between the given three. Nudge applies an impulse which decays over time. If one point is disproportionately far away from a solution, the system nudges itself. The system can always be stabilized by increasing the drag. Equilibrium positions are not always solutions to the problem. To Do: Add wander behavior. Hone the seek behavior for more rapid solution and guessing. ___________ [list=1] [*]Geometric solution: [url]http://www.geogebratube.org/material/show/id/34645[/url] [*]Differential Solution: a. Seek model (one circle): [url]http://www.geogebratube.org/material/show/id/34821[/url] b. Solution, v.1: [url]http://www.geogebratube.org/material/show/id/34855[/url] [b]→c. Solution v.2, improved[/b] [/list]