Introduction | Using the function phasePortrait | Visualizing the complex plane | Visual structuring - the argument pType | divide graphics device into four regions and adjust plot margins | plot four phase portraits with different choices of pType | divide graphics device into three regions and adjust plot margins | separate title call (R base graphics) for nicer line adjustment, just cosmetics | Be aware of branch cuts | Riemann sphere plots | Fractals | Phase portraits based on a polar chessboard | Aesthetic hints | The par(op) mechanism | Dealing with axes | Device ratio and margins | Technical moreabouts | Ways to provide functions to phasePortrait | Quoted character strings | Function objects | Defining image quality | Temporary files | Parallel processing | Acknowledgments | References