This post adds to my design repeat collections. Most of the files provided are intended as inspiration for DIY.
From Truchet/Smith inspired designs 2 meet ArahPaint
Quilters are familiar with block designs easily found in print and online that technically may be broken down into triangular blocks joined and meeting to form sharp points. 
Truchet, in his publication, used half-square triangles 
and assigned letters to the segments, 
and a PNG to explore, 
that when magnified shows the inevitable doubling of some same color pixels side by side or in sequential rows when drawing in random repeats; it becomes unavoidable. 
A DBJ test knit
Exploring how shapes meet and can be combined to make new shapes: this is a 12X10 file, 
shown in repeat,
and in multiple colors 
makes it easier to identify intersections and secondary shapes
A 12X12 start,
with added colors 
tiled in an adjusted colorway
18X18
24X24
different palette tiling
BW version
When you want to knit no more than 2 colors per row, and large repeats with open spaces are appealing, in this 38X18 file, some same color pixels touching soon become evident, 
in progress 57X58
57X58 BW.
Triangles and blocks forming broken ribbons, 36X34
Tired of horizontal and vertical movement, returning to diagonals, recognizing component shapes with clean edges , 
BW 16X48
knit as single bed fair isle
If broken shape edges are OK, this 24X48 repeat with underlying 8X8 blocks, is usable in punchcard models. Triangles are broken along the diagonal solid lines.
In electronic machines without the capacity of knit from screen or added storage, non repetitive image PNGs may need to be programmed in sequential segments.
When producing items such as scarves, there is an opportunity to play with extending the idea further.
Wolfram world is an online reference explaining the rules for building automata.
Cellular automata charts for knitting, etc. was written by me at a time when I produced a series of pieces inspired by their patterning such as this, knit on the Brother 930, 
with images of earlier automata samples knit on my E6000 shared in My new knitting projects
Triangles can be easily recognized forms when testing designing and related techniques and how textures and aspect scale can vary in machine knitting.
From Geometric shapes on ribber fabrics with tuck stitches 2; knitting with 4 carriages
Translating Passap model book pattern/use on Brother 1
Early posts:
A simple shape, an exercise in DBJ, Brother KM
Double jacquard using punchcard machines