User blog comment:Googleaarex/Bashicu Matrix System Analysis (Part 1)/@comment-25601061-20170726022931

Your analysis is wrong. (0,0,0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(2,2,1) is the limit of the omega-sequence:

So where's the second term in your analysis?
 * (0,0,0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)
 * (0,0,0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(2,2,0)(3,3,1)(4,2,0)
 * (0,0,0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(2,2,0)(3,3,1)(4,2,0)(3,3,0)(4,4,1)(5,3,0)
 * (0,0,0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)(2,2,0)(3,3,1)(4,2,0)(3,3,0)(4,4,1)(5,3,0)(4,4,0)(5,5,1)(6,4,0)