PLEASE NOTE: This document is outdated. New commits changed the way you use the API, and a complete JavaFX front-end has been added.
Mosaic — Also known as: ArtMosaico, Count and Darken, Cuenta Y Sombrea, Fill-a-Pix, Fill-In, Komsu Karala, Magipic, Majipiku, Mosaico, Mosaik, Mozaiek, Nampre Puzzle, Nurie-Puzzle, Oekaki-Pix, Voisimage.
Mosaic is a Minesweeper-like puzzle based on a grid with a pixel-art picture hidden inside. Using logic alone, the solver determines which squares are painted and which should remain empty until the hidden picture is completely exposed.
Each puzzle consists of a grid containing clues in various places. The object is to reveal a hidden picture by painting the squares around each clue so that the number of painted squares, including the square with the clue, matches the value of the clue.
Originally created by Trevor Truran, after inspiration of Conway's Game of Life.
The puzzle was later developed by ConceptisPuzzles under the name Fill-a-Pix, following the "a-pix" pixel art series:
I'll stick to the name "Mosaic" as the general name of this puzzle.
Here are some links to understand the rules of the puzzle — all from ConceptisPuzzles:
- Mosaic Rules
- Animated Solving — Requires Flash
- Basic Logic and Advanced Logic Techniques
- Puzzle Tips
- Puzzle History
There are 3 rules that must be met when creating a Mosaic. Trying to solve them using the API will result in its appropriate exception to be thrown.
- Every cell must have at-least one clue, either surrounding or in itself.
As you can see, the 3 right cells will never be solvable. Trying to solve this with the API will throw:
Exception in thread "main" com.stackexchange.puzzling.user.mordechai.mosaic.solvers.NoClueException: x: 3, y: 0
at com.stackexchange.puzzling.user.mordechai.mosaic.solvers.AbstractSolveAlgorithm.<init>(AbstractSolveAlgorithm.java:37)
at com.stackexchange.puzzling.user.mordechai.mosaic.solvers.RecursionSolver.<init>(RecursionSolver.java:32)
at com.stackexchange.puzzling.user.mordechai.mosaic.solvers.RecursionSolver.<init>(RecursionSolver.java:28)
at com.stackexchange.puzzling.user.mordechai.mosaic.TestPuzzle.main(TestPuzzle.java:14)
- Clues must not contradict.
Since 9 means all cells painted, the 2 will have 3 painted cells, which contradicts with the clue. Trying to solve this with the API will throw:
Exception in thread "main" com.stackexchange.puzzling.user.mordechai.mosaic.solvers.ContradictionException: x: 3, y: 1
at com.stackexchange.puzzling.user.mordechai.mosaic.solvers.RecursionSolver.takeStepImpl(RecursionSolver.java:151)
at com.stackexchange.puzzling.user.mordechai.mosaic.solvers.RecursionSolver.takeStep(RecursionSolver.java:127)
at com.stackexchange.puzzling.user.mordechai.mosaic.solvers.RecursionSolver.run(RecursionSolver.java:90)
at com.stackexchange.puzzling.user.mordechai.mosaic.solvers.RecursionSolver.start(RecursionSolver.java:56)
at com.stackexchange.puzzling.user.mordechai.mosaic.TestPuzzle.main(TestPuzzle.java:23)
- Must have a unique solution.
If not enough clues are given there may be cases where 2 or more possible solutions are all correct according to the clues.
Once again, trying to solve a puzzle like this with this with checkAmbiguity(true), will throw:
Exception in thread "main" com.stackexchange.puzzling.user.mordechai.mosaic.solvers.AmbigiousException: x: 3, y: 1
at com.stackexchange.puzzling.user.mordechai.mosaic.solvers.RecursionSolver.lambda$5(RecursionSolver.java:224)
at com.stackexchange.puzzling.user.mordechai.mosaic.solvers.AbstractSolveAlgorithm.fire(AbstractSolveAlgorithm.java:175)
at com.stackexchange.puzzling.user.mordechai.mosaic.solvers.AbstractSolveAlgorithm.setState(AbstractSolveAlgorithm.java:82)
at com.stackexchange.puzzling.user.mordechai.mosaic.solvers.RecursionSolver.setState(RecursionSolver.java:283)
at com.stackexchange.puzzling.user.mordechai.mosaic.solvers.RecursionSolver.takeStep(RecursionSolver.java:119)
at com.stackexchange.puzzling.user.mordechai.mosaic.solvers.RecursionSolver.takeStep(RecursionSolver.java:104)
at com.stackexchange.puzzling.user.mordechai.mosaic.solvers.RecursionSolver.takeStep(RecursionSolver.java:104)
at com.stackexchange.puzzling.user.mordechai.mosaic.solvers.RecursionSolver.run(RecursionSolver.java:90)
at com.stackexchange.puzzling.user.mordechai.mosaic.solvers.RecursionSolver.start(RecursionSolver.java:56)
at com.stackexchange.puzzling.user.mordechai.mosaic.TestPuzzle.main(TestPuzzle.java:23)
The entry point is the class Mosaic that takes a java.awt.Image, URL or a Grid<Clue> - the logical representation of a grid used internally in Mosaic - as its constructor's parameters. The Grid will be filled with Clues. Here's the Clue class:
package com.stackexchange.puzzling.user.mordechai.mosaic;
public class Clue {
private Fill fill = Fill.EMPTY;
private int clue = -1;
private boolean isPixel;
public Clue(Fill fill, int clue, boolean isPixel) {
this.fill = fill;
this.clue = clue;
this.isPixel = isPixel;
}
public Clue(boolean isPixel) {
this.isPixel = isPixel;
}
public Clue(Clue other) {
if (other == null)
return;
this.fill = other.fill;
this.clue = other.clue;
this.isPixel = other.isPixel;
}
public Clue() {
}
public Fill getFill() {
return fill;
}
public int getClue() {
return clue;
}
public boolean isPixel() {
return isPixel;
}
public void setFill(Fill fill) {
this.fill = fill;
}
public void setClue(int clue) {
this.clue = clue;
}
public void setIsPixel(boolean b) {
isPixel = b;
}
}
Fill is an enum with values FILLED, EMPTY, X;
1.1 Filling Clues
The Mosaic class itself just sets the isPixel of each clue according to the image, but the actual clues is up to the programmer to do. Mosaic has a method:
public void putClues(ClueGenerator generator)
Which helps fill them up neatly.
ClueGenerator is a functional interface:
package com.stackexchange.puzzling.user.mordechai.mosaic;
import com.stackexchange.puzzling.user.mordechai.grid.Grid;
public interface ClueGenerator {
boolean shouldGenerate(Grid<Clue> grid, int x, int y, int iteration);
default int iterations() {
return 0;
}
}
Here's an example of creating and filling the clues with a checkerboard design:
Mosaic m = new Mosaic(getClass().getResource("empty-8x8.png"));
// empty-50x50.png is just a white empty image of size 8,8
m.putClues((grid, x, y, iteration) -> (x+y) % 2 == 0);
System.out.println(m.getGrid().toGridString(
clue -> " " + (clue.getClue() == -1 ? " " : clue.getClue()),
false)); // true would return with grid-lines
The above code prints to the console:
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
You can as well do random fills or even make the clues be an image itself:
Grid grid = new Grid<>(20, 20);
grid.fill(Clue::new);
Mosaic m = new Mosaic(grid);
BufferedImage image = new BufferedImage(20, 20, BufferedImage.TYPE_INT_RGB);
Graphics g = image.getGraphics();
g.setColor(Color.WHITE);
g.fillRect(0, 0, 20, 20);
g.setColor(Color.BLACK);
g.setFont(new Font("Dialog", Font.BOLD, 25));
g.drawString("?", 2, 19);
g.dispose();
Mosaic q = new Mosaic(image);
m.putClues((gr, x, y, iteration) -> q.getGrid().get(x, y).isPixel() || (x+y) % 4 == 0);
System.out.println(m.getGrid().toGridString(
clue -> " " + (clue.getClue() == -1 ? " " : clue.getClue()),
false));
Results:
0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0
0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0
0 0 0 0 0
Ideas are virtually endless, show your creativity here.
1.2 Iterations
In some cases you will want to repeatedly iterate over the grid when filling the clues until some precondition is met (e.g. Fill randomly, then repeat and check if a cell has a missing clue).
There's an overloaded version of putClues():
public void putClues(ClueGenerator generator, int iterations)
The process will repeat n times according to iterations. You can get the current iteration in the last argument of the clue generator.
In the event that you want to write a general, full concrete implementation of ClueGenerator that heavily relies in the amount of iterations, you can override the default iterations() method. Any number greater that zero will always have precedence over the iterations parameter in putClues(). Zero or below will either use the iterations param or default to 1 if the first overload is used.
To the current time, I've implemented one solve algorithm, namely RecursionSolver. As its name tells, it uses recursion. The regular case doesn't really require recursion to solve; it's the Advanced Logic problems that recursion will be used for.
Using it is easy, just create an instance, pass the Mosaic as constructor argument and start.
Mosaic m = new Mosaic(...);
RecursionSolver rs = new RecursionSolver(m);
rs.start();
You can then output the results to the console:
System.out.println(m.getGrid().toGridString(clue -> " " + clue.getFill(), false));
And a report:
System.out.println(rs.getReport());
2.1 Uniqueness
As explained earlier, puzzles must follow some rules to be valid. Contradictions and missing clues are detected easily, but uniqueness requires to try all valid solutions and check if more than one is found.
For this reason, I've designed the solver that uniqueness detection is off by default. You can toggle that behaviour:
rs.checkAmbiguity(aBoolean);
After you've created a Mosaic but you want to put it into Excel, you have to print a CSV version and just copy-paste it:
System.out.println(m.getGrid().toGridString(
clue -> (clue.getClue() == -1 ? " " : clue.getClue()) + "\t" ,
false));
My experience is that you should size the cells: Width: 1.86, Height: 13.5
Much hard work has gone to develop this API. You are free to use it without limit and even create your own user interface version. If you publish a puzzle created by this API publicly on the Internet (intentionally excludes for private use), you should link this repository.