The "compass rose pattern" is known to appear in the phase portraits, or scatter diagrams, of the high-frequency returns of financial series. We first show that this pattern is also present in the returns of spot electricity prices. Early researchers investigating these phenomena hoped that these patterns signaled the presence of rich dynamics, possibly chaotic or fractal in nature. Although there is a definite autoregressive and conditional heteroscedasticity structure in electricity returns, we find that after simple filtering no pattern remains. While the series is non-normal in terms of their distribution and statistical tests fail to identify significant chaos, there is evidence of fractal structures in periodic price returns when measured over the trading day. The phase diagram of the filtered returns provides a useful visual check on independence, a property necessary for pricing and trading derivatives and portfolio construction, as well as providing useful insights into the market dynamics.