Neural networks are revolutionizing artificial intelligence (AI), but suffer from poor explainability; for example, recurrent neural networks (RNNs) hold massive potential for sequential or real-time information processing, but their recurrences exacerbate explainability issues and make understanding or predicting RNN behavior difficult. One way to explain neural networks is SplineCam, which illustrates a 2D projection of a neural network’s analytical form—however, it does not natively support RNNs. We circumvent this limitation by using linearly-recurrent RNNs, which can be unrolled into feedforward networks. We apply the resulting method, dubbed SplineCam-Linear-RNN, to linearly-recurrent RNNs trained on biosignal data and sequential MNIST. Our procedure enables: (1) unprecedented visualization of the decision boundary and complexity of an RNN, and (2) visualization of the frequency sensitivity of RNNs around individual data points.