Data visualization for pattern analysis (language-independent, but R preferred)
I would use a visual analysis. Since you know there is a repetition every 256 bytes, create an image 256 pixels wide by however many deep, and encode the data using brightness. In (i)python it would look like this:

import os, numpy, matplotlib.pyplot as plt

%matplotlib inline

def read_in_chunks(infile, chunk_size=256):
    while True:
        chunk = infile.read(chunk_size)
        if chunk:
            yield chunk
        else:
            # The chunk was empty, which means we're at the end
            # of the file
            return

fname = 'enter something here'
srcfile = open(fname, 'rb')
height = 1 + os.path.getsize(fname)/256
data = numpy.zeros((height, 256), dtype=numpy.uint8)    

for i, line in enumerate(read_in_chunks(srcfile)):
    vals = list(map(int, line))
    data[i,:len(vals)] = vals

plt.imshow(data, aspect=1e-2);


This is what a PDF looks like:



A 256 byte periodic pattern would have manifested itself as vertical lines. Except for the header and tail it looks pretty noisy.