Grid Patterns using 2D Array Indexes: i, j

The image below uses logic: color factor k = min( i, j) in regions 1 and 4. In addition, there are diagonal color gradients blocks in regions 2 and 3. The primary block unit has been repeated 4 times across adjacent regions, where scale( scaleX, scaleY) has been used to create mirror-images of the basic unit

Diagonal Color Gradients

Define variable k to determine color pattern.

In the image above, we see a diagonal color gradient in both the foreground and background colors. The logic associated with this can be seen in the image below. If we define a new variable: int k = i + j; , where k is the sum of the i, j index variables, we see that the value of k increases along the grid's diagonal direction. Then we can use k as a factor to determine the fill color.

Color Gradient Logic:

Using the sum of grid indexes for color logic gives us a simple approach to create complex patterns. We can observe a pattern that forms when we consider i,j indexes of each cell: if we add i + j indexes for a cell, then neighboring cells along diagonal lines have equal values of i + j. We can use this relationship to determine fill values for cells, so we can create a gradient fill diagonally across a grid of cells.

      int k= i + j; //i,j are for-loop indexes
      fill( 150 + (k * 10) );  //gradient logic

Odd-Even Gradient Logic

We can also use this sum variable: k for determining odd-even logic. When we use the modulus operator %, we focus on the remainder component, so when k%2 has no remainder ( k%2 == 0 ), we have a way to implement odd-even logic in our patterns. In the image below, we've combined it with the gradient color fill logic. If we have an odd item, then we use a light gray fill(240), otherwise, we use our gradient logic to create our fill.

int k= i + j; //i,j are for-loop indexes
if(k % 2 == 0){
    fill( 100 + k *10); //gradient logic
}
else{
    fill(240); //light gray
}

Random Patterning Logic

In the images below, we can see that there are 2 different design units, shape1 has 2 colored vertically-stacked triangles on a dark background, shape 2 is a rotation - so the colored triangles have left/right orientation. By randomly selecting between these units, we have an additional design pattern.

Shape1 ... Shape2

Logic for Randomized 2-pattern arrangement:

We can use the Processing random(min,max ) function to simulate random events. We define and initialize a random variable: rand that will be assigned a decimal value between 0.0 and 2.0. We determine that if rand > 1, then we vertexPattern1( ), like a coin flip, roughly half the time we'll have rand < 1 and instead we'll vertexPattern2( ).

//Code snippet for random logic to determine which shape is created.
float rand= random(0,2);
if(rand > 1){
    vertexPattern1(size, foreground, background);
}
else{
    vertexPattern2(size, foreground, background);
}

Other Patterns based on i, j index

min( i, j)

The logic for the image below uses the fact that along square shaped sections, like the outer top-row and the left-column both share the feature that the minimum value of the i,j index for each element is 0.

k = min( i, j);

max( i, j);

The logic for the image below uses the fact that along square shaped sections, like the outer bottom-row and the right-column both share the feature that the max value of the i,j index for each element is 5. The lerpColor( ) function can use a factor like k to determine color for each grid cell.

Boolean Conditional Modulus Logic: Mod5 or Mod7

//Mod 5 or Mod 7

      int k= i + j;
      if(k % 5 == 0 || k% 7 ==0){
        fill( 100 + k *10);
      }
      else{
        fill(240);
      }
   

Multiplication with Modulus 3,5

      int k= i * j;
      if(k % 3 == 0 || k% 5 ==0){
         fill( 100 + k * 5);
      }
      else{
         fill(240);
      }