What I found interesting is that I couldn't get a proper fit with the same parameters you showed... however, I could 'speed up' the learning by regenerating the data during the learning process.
It may just be that 'batched cumulative learning' (I don't know if there is already a term for this) gets a better fit than just learning from a smaller set of data.
Edit: Did a quick test; regenerating about every 50 and 100 iterations, and conversion does seem faster (at least, when a clear spiral is formed). https://imgur.com/a/OPjXb
Regenerating the data is kind of cheating; it is as if you were given twice the amount of data.
In a normal situation, you obtain a list of input / output (say, images as input, a digit as output, for learning handwritten digits). You separate it between training data (which actually improves the net) and testing data (to detect overfitting), and you don't get more data than that.
Here, you can generate more data for free, as we have the function we want to approximate. Having more data will often result in a better result and faster convergence.
It may just be that 'batched cumulative learning' (I don't know if there is already a term for this) gets a better fit than just learning from a smaller set of data.
Edit: Did a quick test; regenerating about every 50 and 100 iterations, and conversion does seem faster (at least, when a clear spiral is formed). https://imgur.com/a/OPjXb