Pattern Games

Learning Objectives Define recursion and identify its base case and recursive step in a pattern-generating function. Trace the execution of a simple recursive algorithm to predict the visual pattern it creates. Implement a basic recursive function to draw a fractal pattern, like a branching tree. Explain the concept of a cellular automaton, including its components: grid, states, and rules. Manually calculate the next generation of a simple 1D cellular automaton based on a given rule set. Modify the rules or parameters of a pattern-generating program to create new and unique visual outputs. Have you ever wondered how video games can generate endless, complex landscapes or how a tiny seed of code can grow into a beautiful, intricate snowflake pattern? ❄️ In this lesson, we&#...

TermDefinitionExample RecursionA programming technique where a function calls itself in order to solve a problem. It breaks a large problem into smaller, identical sub-problems.To calculate a factorial (5!), you solve 5 * 4!. To solve 4!, you solve 4 * 3!, and so on, until you reach the simple case of 1! which is 1. Base CaseThe condition within a recursive function that stops it from calling itself, preventing an infinite loop.In a recursive function to draw a tree, the base case might be `if the branch length is less than 5 pixels, stop drawing`. Recursive StepThe part of a recursive function where it calls itself, typically with a modified argument that moves it closer to the base case.In the tree-drawing function, the recursive step would be `draw a trunk, then call the function again...

Recursive Function Structure function recursivePattern(parameters): // Base Case if (condition is met): stop and return // Action do something (e.g., draw a line) // Recursive Step recursivePattern(modified parameters) recursivePattern(other modified parameters) Use this structure to create patterns that are self-similar. The base case is critical to prevent the program from crashing. The recursive step breaks the problem down into smaller versions of itself. Cellular Automaton Update Logic For each cell in the grid: 1. Get the states of its neighbors. 2. Combine neighbor states into a pattern (e.g., '101'). 3. Look up this pattern in a rule set to find the cell's next state. 4. Store the new state in a temporary new grid. After all c...