agt:

Isn’t it structurally similar to an RNN, because we are feeding the output of the convolution into itself over a number of steps in sequence?


CNNs process spatial information while RNNs process temporal information. While they both have hidden states (and parameters), the purpose and application is completely different.1-D CNNs are sometimes applied to text data, but in most cases, they cannot carry the context information the way RNNs do (better techniques are available now).



 agt:

If my input grid’s length is variable


In most cases, you would like to pad or trim your input image to the same size to ensure consistent dimensions before feeding to your network.
Try implementing what you’re thinking and we can discuss more.