Nativetexan the name of your technique is also 'fractured'. But in your case, you used identical pieces of fabric cut at certain points, The first set of strips would be labeled A1, A2 etc. The second set of strips (cut slightly differently) would be labeled B1,B2 etc. Then you sewed them back together A1, B1,A2,B2 etc. I think they may also be recut and resewed horizontally as well.
The 'fractured' picture referred to by the OP is a photo that has been super enlarged and then cut into sections. One section is given to each participant to reproduce using fabric. Then those fabric sections are sewed together.