If you are looking for an explicit mathematical (analytic geometrical etc.) formula which would generate the geometrical shape (the pattern) that you define as the one which would compress least under a given JPEG encoder implementation; I haven't heard of such a formula. May be there is but as I said I haven't heard of one such.
However, the way you ask this question is not the most proper approach given the theoretical concepts behind the JPEG image compression algorithms. If you look at a generic JPEG encoder, you would see that there are a number of blocks such as the DCT, Quantizer and VLC Huffman encoder.
I won't go into the details of the theoretical analysis of those blocks and the mechanism of how the associated compression is physically achieved. However I will describe the charactheristic of the shape which would produce more bits than others under a given encoder:
The shape which would result in the largest JPEG encoded bitstream is the one, which, after its DCT is taken, produces least number of consequitive zeros and largest amplitude coefficients after the DCT coefficients are quantized by a selected weighting matrix.
So which image would do that? It depends on the weighting matrix and DCT. If you select a human visual system based weighting matrix then the image must have excess high frequency contets. This means that The image must be composed of sharp and short duration black and white passages.
Its orientation could also matter because of the zig-zag scannig pattern of eth DCT coefficients. But its hard to be sure without further analysis.
Consequently a white noise image with high dynamic range would produce quite large file size as its DCT would be ineffecitve to reduce its frequency content to low frequency coefficients.