The design of concentric squares is most often seen as a block. Above a four-block version from Western Kentucky University.
Most of the pictures are from online auctions.
Typical taste in fabrics after 1900
The pattern looks to have developed about 1880 or so.
The new BlockBase+ tells us the Ladies Art Company
published the pattern as White House Steps.
#221 is in their early catalog, 1890s, and that's probably
the source for many of these quilts.
Although you see earlier versions, this one in wools
and combination fabrics, is perhaps the 1880s.
Logs are folded and attached to a foundation square.
In its organized fashion a very neat and orderly design.
Minimal version.
But not always
Arlonzia Pettway, 1982, from the book
Gees Bend: the Women & Their Quilts
Gearldine Westbrook, 1982
William Ferris, Gees Bend: The Architecture of the Quilt
Traditional bird trap made of sticks.
Louise Tieman has been collecting references to Bird Trap as a name for log cabins and has found several sources, her favorite being police reports where she's found two accounts of Bird Trap quilts being stolen.
"There was also taken a worsted quilt, black and red, of the log-cabin or bird-trap design, with blue buttons sprinkled over it. We hope that everyone seeing this notice will be on the look-out for the quilt, -- as the finding of it may lead to the detection of the thief.”Louise's blog post: http://quiltpapers.blogspot.com/2020/
In 1933 folklorists Vance Randolph & Isabell Spradlin mentioned Bird Trap in "Quilt Names in the Ozarks."
In 1871 the Nashville Union remarked on a fair display with "a bird-trap quilt made of silk that was greatly admired."
But whether Bird Trap refers to a type of log cabin design
is unknown.