A neural network written from scratch, one matrix at a time, training in front of you. No TensorFlow, no autograd, no GPU. Every gradient below comes from the chain rule applied by hand.
A fully connected network trained by minibatch gradient descent on cross entropy loss. The forward pass is a chain of z = Wx + b followed by a nonlinearity; the backward pass walks the same chain in reverse, multiplying by each layer's local derivative and accumulating dW and db along the way. Momentum smooths the updates. Weights start from He or Xavier scaling depending on the activation you pick, which is why a fresh initialisation converges instead of stalling.
The boundary is drawn by running the network over a grid of points and shading each one by its output, so you are seeing the function the network currently represents rather than an animation of it. Raise the noise until the classes overlap and you can watch it memorise instead of generalise, which is what regularisation is there to punish.