You win if you get 4 in a row within a "pizza slice".
You win if you get 4 in a row within a concentric circle.
You win if you get 4 in a spiral pattern. The spiral here runs counter-clockwise; the spiral can run either counter-clockwise or clockwise.
You can download TicTacToe.java as a starting point in completing this program. Much of the program is already written. Several sections of code are incomplete and you can write those. Instructions for writing code are given in the Java file.
A JAR file for a complete Circular Tic-Tac-Toe game is available. Click here to download the JAR file TicTacToe.jar. Then double-click on it and the game should run, but there's no guarantee.