And here are the individual terms (not summed). The colors are still related to those in the previous toot, but I mixed in a little bit of black to ensure a reasonable amount of contrast with the white background.
On the left: each monomial of the decomposition.
On the right: same, but divided by the exponential function again.
As a follow-up to yesterday's post, here's the same visualization, but with everything normalized, i.e. divided by the exponential function. I haven't included the reversed version (with low-order terms at the top) this time, because now it would just amount to flipping the figure upside down.
Decomposition of the exponential function as the sum:
x⁰/0! + x¹/1! + x²/2! + x³/3! + ...
* On the left, low-order terms are at the bottom.
* On the right, low-order terms are at the top.
Same color in both pictures corresponds to the same monomial.
Crazy how different the two pictures look, even though they represent the same decomposition!
Grégoire Locqueville