Create the least compressible picture "A picture is worth a thousand words"—so the old saying goes. The average word is about four characters long, so a picture conveys 4kB of information. But how much entropy, rather than information, can a picture convey?

Your task is to generate an image, exactly 4,000 bytes in size, with the highest entropy possible. You may use any language, libraries, or image format you choose, and you may output to the console or to a file so long as you upload your image here.

Scoring

Your score is the compression ratio (4000 ÷ compressed size) when your image is compressed with GNU tar version 1.28 and gzip version 1.6, using the DEFLATE algorithm and default settings — specifically, the command tar -czvf out.tar.gz image. The smallest compression ratio wins.
0.9514747859 (4204-byte output)



Note: the image above is not the actual file I used, but it is the image. 

Here is a hexdump of the file: https://gist.github.com/pommicket/cf2982e8ecf09a4de89d3a849526c64b

The file is in the netpbm format, and can be generated with this C code:

#include &lt;stdio.h&gt;
#include &lt;stdlib.h&gt;

int main(int argc, char **argv) {
    if (argc &lt; 2) {
        fprintf(stderr, "Please pass in seed.\n");
        return EXIT_FAILURE;
    }
    srand(atoi(argv[1]));
    FILE *fp = fopen("image.pgm", "w");
    int width = 2, height = 1993;
    fprintf(fp, "P5 %d %d 255 ", width, height);
    for (int i = 0; i &lt; width * height; i++) {
        fputc(rand() &amp; 0xFF, fp);
    }
    fclose(fp);
    return 0;
}


The random seed must be passed into the program. After trying some seeds, I got one which produced a 4204 byte gzipped file. As Nnnes pointed out, tar will include metadata in the file, so your results might differ from mine.

netpbm isn't supported everywhere, but it works with imagemagick's convert (so just do convert image.pgm image.png to turn it into a png).

Why this image/format?

A file which consists of entirely random bytes is very hard to compress (in fact, any possible compression algorithm will do on average, no better than not compressing for random files). The content of the actual file is just P5 2 1993 followed by 3986 random bytes, which is why gzip has such a hard time compressing it.