Think Like a Coder: Programming a Robot Artist

In the heart of the 198forest, Ethic and Hedge face a new challenge in their quest to save the world. Their mission: to acquire the second artifact, hidden within a heavily guarded tower. To get there, they need a diversion, and Octavia, the director of the colony, has a plan: a little well-intentioned vandalism.

The residents of the forest are obsessed with displaying self-portraits – squares of art with an odd number of pixels. Helper-bots dutifully hang these portraits for all to admire. Hedge's task is to deface these paintings with an "X", but his painting processor requires precise instructions. How can Ethic program Hedge to create this distraction?

The Challenge: Painting an "X"

Hedge can only fill in one pixel at a time, moving forward or making 90-degree turns. The challenge is to devise a set of instructions that works for any square grid, regardless of its size. This highlights a core strength of programming: solving a whole class of problems at once.

Breaking Down the Problem

To start, consider a single square. Hedge can measure the length of its sides and store that value as a variable. The goal is to develop a plan for Hedge to paint an "X", pixel by pixel. There are multiple solutions, but let's explore two approaches.

Method 1: The Typewriter Approach

Imagine Hedge moving row by row, like a typewriter. For a 9x9 pixel painting, in the first row, he'd paint, skip 7 pixels, and paint again. In the second row, he'd skip 1, paint, skip 5, and paint. The pattern is that for each row, the pixels skipped at the beginning increase by one, and the pixels skipped in the middle decrease by two.

• Pros: Adaptable to filling in any pattern.
• Cons: Requires complex logic to handle the center and reverse the process.

Method 2: Concentric Squares

The key insight here is to view the grid as a series of concentric squares. Each square follows the same pattern: painted pixels in the corners, unaltered pixels in between. If we can program Hedge to paint one nested square, transition to the next, and repeat, we can paint them all.

1. Paint the outermost square: Start in a corner, paint that pixel, move forward n-1 spaces (where n is the length of the painting), paint another pixel, and turn right. Repeat this process.
2. Move to the next square: Move forward one less space, turn right, and move forward once. Hedge is now in the next concentric square.
3. Repeat: Each square is n-2 pixels smaller than the last. Follow this spiral pattern to the center using a loop and a variable to track the distance Hedge should move.

This method uses a loop and a variable to track how far Hedge should fly.

• Pros: Simplicity of finding a pattern and reusing the same logic.
• Cons: Less adaptable to other patterns.

Which Method is Better?

The best method depends on your priorities. The spiral approach offers simplicity and consistent logic, while the typewriter approach provides a more generalized solution. Either method will work for Ethic's purpose.

The Diversion

Hedge rapidly defaces the portraits, and cries of anguish erupt throughout the forest. The garrison abandons its post to quell the unrest, allowing Ethic, Hedge, and Octavia to slip past and face the dangers of the gorge leading to the tower. The success of their mission now hinges on navigating the perilous path ahead.

In summary, the challenge of programming Hedge to paint an "X" highlights the power of computational thinking and the ability to solve complex problems by breaking them down into smaller, manageable steps. By identifying patterns and creating reusable code, Ethic can overcome obstacles and continue her quest to save the world.