49683 49280 49131 bytes

Generated by this Python code. I designed the PNG scanlines by hand to be encoded using repetitions of short sequences that compress well. I’ve now written enough of a custom DEFLATE encoder to let me decide where to split the compressed blocks (saving 149 bytes compared to zlib).

import itertools import struct import zlib def lsb(b, n): assert 0 <= n < 1 << b return f"{n:0{b}b}"[::-1] if b else "" def huffman(lengths, letter): code = sum( 1 << lengths[letter] - length for other_letter, length in lengths.items() if (length, other_letter) < (lengths[letter], letter) ) return f"{code:0{lengths[letter]}b}" def literal(letter): assert 0 <= letter < 256 return huffman(literals, letter) def end(): return huffman(literals, 256) def match(length, distance): assert 3 <= length <= 258 assert 1 <= distance <= 32768 if length == 258: bits = huffman(literals, 285) else: i = max(0, (length - 3).bit_length() - 3) bits = huffman(literals, 4 * i + 257 + (length - 3 >> i)) + lsb( i, length - 3 & ~(~0 << i) ) j = max(0, (distance - 1).bit_length() - 2) bits += huffman(distances, 2 * j + (distance - 1 >> j)) + lsb( j, distance - 1 & ~(~0 << j) ) return bits code_length_order = [16, 17, 18, 0, 8, 7, 9, 6, 10, 5, 11, 4, 12, 3, 13, 2, 14, 1, 15] def encode_lengths(): hlit = max(literals) + 1 - 257 hdist = max(distances) + 1 - 1 hclen = max(map(code_length_order.index, code_lengths)) + 1 - 4 bits = lsb(5, hlit) + lsb(5, hdist) + lsb(4, hclen) for i in code_length_order[: hclen + 4]: bits += lsb(3, code_lengths.get(i, 0)) for length, group in itertools.groupby( [literals.get(i, 0) for i in range(hlit + 257)] + [distances.get(i, 0) for i in range(hdist + 1)], lambda length: length, ): n = len(list(group)) while length == 0 and 18 in code_lengths and n >= 11: bits += huffman(code_lengths, 18) + lsb(7, min(n - 11, 127)) n -= min(n - 11, 127) + 11 while length == 0 and 17 in code_lengths and n >= 3: bits += huffman(code_lengths, 17) + lsb(3, min(n - 3, 7)) n -= min(n - 3, 7) + 3 # not implemented: 16 (copy previous code) bits += huffman(code_lengths, length) * n return bits png_header = struct.pack( "!IIBBBBB", 2 ** 16, # width 2 ** 8, # height 8, # bit depth 2, # color type 0, # compression method 0, # filter method 0, # interlace method ) zlib_header = struct.pack( "!BB", 8 | 7 << 4, # compression method, compression info 26 | 0 << 5 | 3 << 6, # check bits, preset dictionary, compression level ) literals = {1: 2, 2: 4, 256: 4, 268: 4, 284: 4, 285: 1} distances = {2: 1, 18: 1} code_lengths = {0: 3, 1: 2, 2: 3, 4: 2, 18: 2} bits = "0" # start non-final block bits += lsb(2, 2) # compressed with dynamic Huffman codes bits += encode_lengths() bits += literal(1) + literal(1) + literal(1) + literal(2) + literal(1) + literal(2) bits += 2 * match(258, 3) bits += match(248, 3) bits += 5 * ( match(258, 768) + match(258, 3) + 42 * (match(258, 768) + 2 * match(258, 3)) ) bits += match(258, 768) + match(258, 3) + 39 * (match(258, 768) + 2 * match(258, 3)) bits += match(17, 3) bits += end() literals = {1: 3, 256: 3, 264: 3, 279: 3, 285: 1} distances = {0: 1, 2: 1} code_lengths = {0: 3, 1: 2, 3: 2, 17: 3, 18: 2} bits += "1" # start final block bits += lsb(2, 2) # compressed with dynamic Huffman codes bits += encode_lengths() bits += 96780 * match(258, 1) bits += match(105, 1) bits += literal(1) + literal(1) bits += 762 * match(258, 3) bits += match(10, 3) bits += 96780 * match(258, 1) bits += match(102, 1) bits += end() bits += -len(bits) % 8 * "0" compressed = int(bits[::-1], 2).to_bytes((len(bits) + 7) // 8, "little") decompressed = zlib.decompress(compressed, wbits=-15) assert decompressed == bytes( [1, *(2 ** 8) * [1, 1, 2, *(2 ** 8 - 1) * [1, 2, 2]]] + (2 ** 7 - 1) * [2, *2 ** 16 * [2, 2, 2]] + [2, *2 ** 16 * [2, 1, 1]] + (2 ** 7 - 1) * [2, *2 ** 16 * [2, 2, 2]] ) zlib_checksum = struct.pack("!I", zlib.adler32(decompressed)) png_data = zlib_header + compressed + zlib_checksum png = b"\x89PNG\r\n\x1a\n" for type, data in [(b"IHDR", png_header), (b"IDAT", png_data), (b"IEND", b"")]: crc = 0xFFFFFFFF for byte in type + data: crc ^= byte for bit in range(8): crc = 0xEDB88320 * (crc & 1) ^ crc >> 1 crc ^= 0xFFFFFFFF png += struct.pack("!I4s", len(data), type) + data + struct.pack("!I", crc) print(len(png)) with open("rgb.png", "wb") as f: f.write(png) 

Try it online!

(Note: many PNG readers accept an image missing the IEND chunk, but it is required by the PNG specification so I have included it.)

256x65536, 49909 bytes

^{In my experience Google Chrome is the best tool to view this image.}

The red channel starts at 255 in the first row and decreases by 1 each row.
The green channel slowly decreases from 255 to 0 in every row and the blue channel repeatly decreases from 255 to 0.

Generated by the following code in Python 3 with numpy and imageio:

import os import imageio import numpy as np FILENAME = 'out.png' DTYPE = np.uint8 values = np.arange(255, -1, -1, dtype=DTYPE) image = np.empty((256, 256**2, 3), dtype=DTYPE) image[..., 0] = values[:, np.newaxis] # r image[..., 1] = np.repeat(values, 256) # g image[..., 2] = np.tile(values, 256) # b # Verify that all colors are present (slow) # assert len(np.unique(image.reshape(256**3, 3), axis=0)) == 256 ** 3 imageio.imwrite(FILENAME, image) os.system('wc ' + FILENAME) 

I tried to reduce the file size with zopflipng, but even after 50 minutes of running it provided no improvement.