017 min
Encode a mark
Draw an L and translate each cell into 0 or 1.
Ask: “Could the machine reconstruct the picture from all 25 values?”
Listen for: “Yes, if it knows the cell order.”
Brightlab
brightlab.Made for curious mindsbrightlab.Made for curious mindsBrightlab
Year 3 · Representation
What does a picture lose when we turn it into numbers?
Go to the investigation ↓
Investigate with Wattle the wombatA representation collision exhibit with an improved feature and its limits.
Can two different pictures have the same short description?
A digital picture can be represented as a grid of numbers. This lab uses 0 for an empty pixel and 1 for a filled pixel. A smaller representation keeps only the sum of each row. That saves information space but loses where pixels sit inside a row. Two different pictures can therefore have identical row summaries. A useful feature must preserve the differences relevant to our task.
Before this lesson: Count filled squares in a small grid. Useful earlier investigations: The sorting stream.
A digital picture can be represented as a grid of numbers. This lab uses 0 for an empty pixel and 1 for a filled pixel. A smaller representation keeps only the sum of each row. That saves information space but loses where pixels sit inside a row. Two different pictures can therefore have identical row summaries. A useful feature must preserve the differences relevant to our task.
Count filled squares in a small grid. Useful earlier investigations: The sorting stream.
Print two 5 by 5 grids. Prepare an L shape and its horizontal reflection. Calculate row sums in advance to show why they collide. Check keyboard access to every pixel cell.
ACARA V9 AI curriculum connection ↗ · Technologies ↗
A complete teaching sequence · 55 minutes
Draw an L and translate each cell into 0 or 1.
Ask: “Could the machine reconstruct the picture from all 25 values?”
Listen for: “Yes, if it knows the cell order.”
Predict whether reflecting the L changes its row totals before using the mirror control.
Ask: “Which information do row totals keep?”
Listen for: “How many marks, but not their columns.”
Edit cells and inspect the matrix, row bars and column totals. Keep row totals fixed while moving a pixel sideways.
Ask: “What changed in the picture but stayed in the summary?”
Listen for: “The pixel position changed; the row total did not.”
Use the reflected image edge case. Confirm all row totals match even though orientation differs.
Ask: “Can a row-only classifier tell left from right here?”
Listen for: “No, its inputs are identical.”
Choose column totals or a left-half count. Test both original images plus a third image and state any remaining collision.
Ask: “Does your extra feature preserve what this task needs?”
Listen for: “It separates these two orientations.”
Collect two grids, their totals and a feature proposal.
Ask: “Did we prove the feature works for every image?”
Listen for: “No; we tested three and can still find collisions.”
A computer receives a whole object.
An L and its reflection have equal row sums but different orientations. Identical representations force a row-only model to treat them alike.
Add a column-based feature and test whether it separates the pair; then search for another collision.
Ask learners to produce a collision themselves. If they only repeat the supplied example, change the starting image and require a new pair.
| Criterion | Beginning | Secure | Extending |
|---|---|---|---|
| Encoding | Draws without linking cells to numbers | Accurately encodes and sums rows | Explains the information discarded |
| Feature design | Adds arbitrary numbers | Adds a feature that separates the pair | Finds and documents a remaining collision |
Start with a 3 by 3 paper grid and move physical counters within a row. Use the larger browser grid with a partner.
Can two images share both row and column totals? Construct a 2 by 2 diagonal swap as a counterexample.
Use abstract marks only; no student images, handwriting samples or photographed work are required.
Shared device? Turn remembering off. A project file lets you continue on another device.
Your browser is the laboratory
Predict whether a horizontal mirror changes the row-sum representation.
The 5×5 starting image has a vertical stroke in column 2 and a bottom stroke in columns 1–4. Each row is summarised by the count of filled cells. Predict what a horizontal mirror changes.
The experiment opens after your prediction.
There is no penalty for being surprised.
Apple Silicon · PyTorch MPS
Enumerate or sample many binary images and group them by row-sum signatures; measure collision rates when column features are added.
Students extend the experiment in teams, documenting parameters, outputs and limitations.
The bundle contains lesson-specific working code, a configuration file, a reactive notebook, a deterministic CPU check and hardware setup instructions. Acceleration is reported only after a tensor operation and result read-back succeed.
Download Mac Studio investigation ↓unzip y3-pixels-mac-pathway.zip -d y3-pixels-mac cd y3-pixels-mac bash setup-mac.sh source .venv/bin/activate python experiment.py --device mps --output results marimo edit notebook.py
CPU and available-device execution status is recorded in the downloaded README and validation report. DGX Spark execution requires that hardware; static validation alone does not establish GPU compatibility or performance. The browser lesson remains fully available without this extension.
NVIDIA DGX Spark · PyTorch CUDA
Enumerate or sample many binary images and group them by row-sum signatures; measure collision rates when column features are added.
Students extend the experiment in teams, documenting parameters, outputs and limitations.
The bundle contains lesson-specific working code, a configuration file, a reactive notebook, a deterministic CPU check and hardware setup instructions. Acceleration is reported only after a tensor operation and result read-back succeed.
Download DGX Spark investigation ↓unzip y3-pixels-dgx-pathway.zip -d y3-pixels-dgx cd y3-pixels-dgx bash run-dgx.sh # Open the localhost notebook URL printed by the container.
CPU and available-device execution status is recorded in the downloaded README and validation report. DGX Spark execution requires that hardware; static validation alone does not establish GPU compatibility or performance. The browser lesson remains fully available without this extension.
A representation collision exhibit with an improved feature and its limits.
Download the editable handout →