Or are there? Actually, the greenish and blueish areas are the same “aqua” colour. The only difference is that in the greenish areas, aqua is interspersed with orange, whereas in the blueish areas, aqua is interspersed with pink. This becomes clear if you look at the image below, in which all pink has been replaced with orange. By the way, the illusion works equally well in a static image. I just added the rotation to make it look extra cool.
Initially I thought the illusion had to do with colour opponency. There are visual neurons which respond to yellow and are inhibited by blue, and vice versa. Because pink is essentially orange with some added blue, you might think that if aqua is interspersed with pink, it becomes more “yellowish” and, conversely, if aqua is interspersed with orange it becomes more “blueish.” However, on closer inspection the illusion works the other way around: Aqua actually looks more blueish next to pink, than next to orange!
Monnier and Shevell describe an illusion which is similar to the one presented here and offer a tentative explanation. Essentially they say that the colours appear to “spill over.” That is, if aqua is next to pink it simply “borrows” some of the blue that is present in the pink. However, this does not explain why the illusion is less effective if only a single aqua ring is presented in a uniformly orange/ pink background (rather than multiple rings of alternating colours as shown here).
Monnier and Shevell offer an explanation for this as well, but it's a bit tricky. I will do my best to clearly explain my understanding of it. First, they simplify the problem by considering only the level of blue in the image (see (c) and (d) in the image below), after which it becomes clear that, indeed, pink contains much more blue than orange. Next, they posit a specific type of neuron, which responds to the presence of blue in a “center” region and is inhibited (deactivated) by blue in a “surround” region (e). If you superimpose the receptive field of this neuron over the aqua/ orange and aqua/ pink patterns, you see that the aqua/ pink pattern causes more activation (the center contains more blue), but also more inhibition (the surround contains more blue as well). It is not obvious whether this results in a netto increase or decrease in activation. However, my crude simulation confirms that, indeed, the increased activation is not cancelled out by the increased inhibition: The neuron is activated almost 1.5 times as strongly by the aqua/ pink pattern than by the aqua/ orange pattern. Because this neuron signals blueness, aqua does indeed appear more blueish when interspersed with pink. To be honest, I don't find this explanation particularly elegant, but it does appear to work!
Monnier, P., & Shevell, S. K. (2003). Large shifts in color appearance from patterned chromatic backgrounds. Nature Neuroscience, 6(8), 801-802.
Monnier, P., & Shevell, S. K. (2004). Chromatic induction from S-cone patterns. Vision Research, 44(9), 849-856.