Consider a complex function, possibly the Riemann zeta function $\zeta(1/2+it).$ $W_t(x)=\zeta(1/2+it)^{\big(\frac{1}{\log(x)}+\frac{1}{\log(1-x)}\big)}.$ Here $t$ is a time parameter and cycles through values, say from $t\in(1,\infty).$ Letting $x\in(0,1)$ and starting the clock, is this a way to record some zeros of $\zeta(1/2+it)?$ When $\zeta(1/2+it)=0,$ this corresponds to $W_t(x)=0.$ I think $W_t(x)$ will blow up near $x=0,1$ when $\zeta(1/2+it)$ equals zero, and oscillate quietly when $W_t(x)$ is far from a zero. I know that this notion needs to be defined better, and I'm not sure how to do that. My thought was that maybe if you could run a program, the computer could easily pick up when $W_t(x)$ flares up and record the zero? Does this sound plausible?
Here is what a graph looks like for $W_{123}(x).$ So I think we are close to a zero. The closest zero is $122.946829294.$
And here is a graph of $W_{123.7}(x).$
Notice how we are relatively far from a zero. In fact we're about halfway between two zeros, $122.946829294$ and $124.256818554,$ so I think the oscillation should relax and the complex and real curves should have more space between them.