How numpy array full show in jupyter notebook without wrapping?

Two problems seem to mix here:

1. The line breaks introduced by Numpy:

   You can fix these, as already commented and as you already tried, by

   import numpy as np
   np.set_printoptions(linewidth=np.inf)
   

2. The line breaks (or rather, line wraps) introduced by Jupyter:

   You can fix these, following this answer, by

   from IPython.display import display, HTML
   display(HTML("<style>div.jp-OutputArea-output pre {white-space: pre;}</style>"))
   

Together, we have

import numpy as np
from IPython.display import display, HTML

# Avoid line breaks by Jupyter (following https://stackoverflow.com/a/70433850/7395592)
display(HTML("<style>div.jp-OutputArea-output pre {white-space: pre;}</style>"))
# Avoid premature line breaks by Numpy and show all array entries
np.set_printoptions(linewidth=np.inf, threshold=np.inf)
image = np.zeros((256, 256), dtype=np.uint8)
image

This, for me, produces the following output:

Alternatively, as you wrote that your image consists of 0s and 1s only (and thus exclusively of single-digit numbers): you can condense the output even more, by suppressing the commas and spaces, for example like so:

import numpy as np
from IPython.display import display, HTML
# Avoid line breaks by Jupyter (following https://stackoverflow.com/a/70433850/7395592)
display(HTML("<style>div.jp-OutputArea-output pre {white-space: pre;}</style>"))
image = np.zeros((256, 256), dtype=np.uint8)
image_vals = "\n".join(f"[{''.join(str(val) for val in row)}]" for row in image)
print(image_vals)

Which produces the following output (note that I had to use print() in this case):

The only inconvenience that I could find in both cases is that a horizontal scrollbar only appears in the output cell if one scrolls to its very bottom (I tried with Firefox and Chrome).