Sure. These are pretty basic patterns. It would easier to approach it directly as a drawing method, instead of first a 'pattern' that then needs to be drawn. For example the third point pattern could be a drawing tool something like this.

Adapted Code

1. int mx, my;
2. 
   
3. void setup () {
4.   size(900, 700);
5.   background(230);
6. }
7.  
8. void draw() {
9.   strokeWeight(3);
10.   stroke (4);     
11.   fill (0);
12.   if (dist(mx, my, mouseX, mouseY) >= 8) {
13.     ellipse (mouseX, mouseY, 2, 2);
14.     mx = mouseX;
15.     my = mouseY;
16.   }
17. }

Amon beat me to it ;). However i'll post my attempt too. Which will show how to structure the pattern changing. Be warned, i did it while working on something else so it's not the clever approach and i'm sure this can be optimized a lot.Anyway that will give you some clues to figure it out and fix your crosstitch example. Now you just have to mess with that add your other pattenrs, tweak the parameters mess the code then try to optimise. Make it functionnal then make it optimal.

1. boolean isDrawing = false;  // draw only when mouse is Pressed (see mousePressed and mouseReleased below)
2. 
   
3. int Pattern = 1;            // store the Pattern state to know which pattern we need to draw
4. int crossSize = 4;          // cross pattern Size.
5. int dotSize = 4;            // circle dot pattern Size.
6. 
   
7. int offset = dotSize*2;     // offset so that Shapes don't overlap.
8. float tmouseX, tmouseY;     // temp variables to store previous mouse position and to compare distance again to check overlapping shapes.
9. 
   
10. void setup() {
11.   size(400, 400);
12.   background(255);
13.   smooth();
14. }
15. 
    
16. void draw() {
17.   if (isDrawing) {
18.     /* if the distance between the mouse and the mouse previous position
19.      * while pressed is sup at the offset (ie shapes won't overlap)
20.      * let's see which pattern to draw and draw it
21.      */
22.     if (dist(tmouseX, tmouseY, mouseX, mouseY) > offset) {
23.       switch(Pattern) {
24.         // first default pattern
25.       case 1:
26.         noStroke();
27.         fill(0);
28.         ellipse(mouseX, mouseY, dotSize, dotSize);
29.         break;
30.         // Second Square Pattern
31.       case 2 :
32.         offset=crossSize*5;
33.         noFill();
34.         strokeWeight(4);
35.         strokeCap(SQUARE);
36.         stroke(0);
37.         // Square Shape Pattern
38.         beginShape(LINES);
39.         vertex(mouseX - crossSize, mouseY - crossSize);
40.         vertex(mouseX + crossSize, mouseY + crossSize);
41.         vertex(mouseX + crossSize, mouseY - crossSize);
42.         vertex(mouseX - crossSize, mouseY + crossSize);
43.         endShape();
44.         break;
45.       }
46.       tmouseX = mouseX;
47.       tmouseY = mouseY;
48.     }
49.   }
50. }
51. 
    
52. void mousePressed() {
53.   /* switch tricks
54.    * as isDrawing is initialize at false the first press will turn
55.    * this to true and then the release to false and so on
56.    */
57.   isDrawing=!isDrawing;
58. }
59. 
    
60. void mouseReleased() {
61.   isDrawing=!isDrawing;
62. }
63. 
    
64. // Change the Pattern with keyboard key 1,2 and more according to pattern's number
65. void keyPressed() {
66.   switch(key) {
67.   case '1':
68.     Pattern = 1;
69.     break;
70.   case '2':
71.     Pattern = 2;
72.     break;
73.   }
74. }

Thanks to you both.  It does make a beautiful dotted stitch indeed. I am not sure about the other patterns though. They seem more complex. I can't even get the sin wave pattern to stabilize in the draw method...

RandomColorPalette myRandomColorPalette;
Stitches myCrossStitches;
Stitches myFlatStitches;
Stitches myDottedStitches;
Stitches myWavyStitches;

void setup() {  // call the setup function to define initial enviroment properties

  size(900, 700); 
  background(230);

  myRandomColorPalette=new RandomColorPalette (color(255, 255, 255), 100, 0, 0);

  myCrossStitches=new Stitches (color(227, 101, 221), 100, 600, 0, 10);
  myFlatStitches=new Stitches (color(250, 100, 90), 100, 400, 0, 10, 6.6);
  myDottedStitches=new Stitches (color(227, 208, 140), 100, 200, 0, 10, 4);
  myWavyStitches=new Stitches (color(125, 225, 30), 100, 800, 0, 60.0, 40.0, 3.0);
 
}  // end the setup function

void draw () {  // call the draw function

  background(230);

  myRandomColorPalette.display();
  myCrossStitches.display(10);
  myFlatStitches.display(10, 6.6);
  myDottedStitches.display(10, 4);
  myWavyStitches.display(60.0, 40.0, 40.0);
 
}  // end the draw function


abstract class Grid {

  float sizeOfSquares;
  color gridClr;
  float boxPosX;
  float boxPosY;


  Grid(color tempgridClr, float tempsizeOfSquares, float tempBoxPosX, float tempBoxPosY) {

    gridClr=tempgridClr;
    sizeOfSquares=tempsizeOfSquares;
    boxPosX=tempBoxPosX;
    boxPosY=tempBoxPosY;
  }  // end of the constructor


  void display () {

    // initialization of quilt patterns (from Shiffman page 261)

    for (int i=0;i<width;i+=sizeOfSquares) {
      for (int j=0;j<height;j+=sizeOfSquares) {
        fill(gridClr);
        rect(i, j, sizeOfSquares, sizeOfSquares);
      }
    }
  }  // end of the display function


  boolean mouseClickOverBox () {

    if (mousePressed && ((mouseX>boxPosX) && (mouseX<boxPosX+sizeOfSquares) && (mouseY>boxPosY) && (mouseY<boxPosY+sizeOfSquares))) {
      return true;
    }     
    else {      
      return false;
    }
  }
} 


class RandomColorPalette extends Grid {

  RandomColorPalette(color tempgridClr, float tempsizeOfSquares, float tempBoxPosX, float tempBoxPosY) {

    super (tempgridClr, tempsizeOfSquares, tempBoxPosX, tempBoxPosY);

    gridClr=tempgridClr;
    sizeOfSquares=tempsizeOfSquares;
    boxPosX=tempBoxPosX;
    boxPosY=tempBoxPosY;
  } 

  void display () {
    stroke(0);
    fill(gridClr);
    rect (boxPosX, boxPosY, sizeOfSquares, sizeOfSquares);

    if (mouseClickOverBox()) {
      gridClr=(color(random(1, 255), random(1, 255), random(1, 255))); 

      fill (gridClr);
      rect (boxPosX, boxPosY, sizeOfSquares, sizeOfSquares);
    }
  }
}


class Stitches extends RandomColorPalette {

  float clrLine;      
  float strokeClr;      
  int stitchLength;
  float spacing;
  int dotSize;      
  float stitchOffset;
  float stitchSpeed;
  float stitchScalar;
  float stitchAngle;
  float stitchX;      


  // Constructor overloading for four different stitch patterns

  // constructor for cross stitch

  Stitches (color tempgridClr, float tempsizeOfSquares, float tempBoxPosX, float tempBoxPosY, int tempStitchLength) {

    super (tempgridClr, tempsizeOfSquares, tempBoxPosX, tempBoxPosY);


    tempStitchLength= constrain (tempStitchLength, 8, 12);
    gridClr=tempgridClr;
    sizeOfSquares=tempsizeOfSquares;
    boxPosX=tempBoxPosX;
    boxPosY=tempBoxPosY;

    stitchLength=tempStitchLength;
    stitchX=boxPosX+sizeOfSquares/2;
  } 


  // constructor for flat stitch

  Stitches (color tempgridClr, float tempsizeOfSquares, float tempBoxPosX, float tempBoxPosY, int tempStitchLength, float tempSpacing) {

    super (tempgridClr, tempsizeOfSquares, tempBoxPosX, tempBoxPosY);
    tempStitchLength= constrain (tempStitchLength, 8, 12);
    tempSpacing= constrain (tempSpacing, tempStitchLength/5, tempStitchLength*4/5);
    gridClr=tempgridClr;
    sizeOfSquares=tempsizeOfSquares;
    boxPosX=tempBoxPosX;
    boxPosY=tempBoxPosY;
    spacing=tempSpacing;
    stitchLength=tempStitchLength;
    stitchX=boxPosX+sizeOfSquares/2;
  } 


  // constructor for dotted stitch

  Stitches (color tempgridClr, float tempsizeOfSquares, float tempBoxPosX, float tempBoxPosY, int tempSpacing, int tempDotSize) {

    super (tempgridClr, tempsizeOfSquares, tempBoxPosX, tempBoxPosY);

    tempSpacing= constrain (tempSpacing, 8, 12);
    tempDotSize=constrain(tempDotSize, 1, 4);
    gridClr=tempgridClr;
    sizeOfSquares=tempsizeOfSquares;
    boxPosX=tempBoxPosX;
    boxPosY=tempBoxPosY;
    dotSize=tempDotSize;
    spacing=tempSpacing;
    stitchX=boxPosX+sizeOfSquares/2;
  } 



  // constructor for the wavy stitch

  Stitches (color tempgridClr, float tempsizeOfSquares, float tempBoxPosX, float tempBoxPosY, float tempStitchOffset, float tempStitchSpeed, float tempStitchScalar) {

    super (tempgridClr, tempsizeOfSquares, tempBoxPosX, tempBoxPosY);

    tempStitchOffset=constrain (tempStitchOffset, 8, 12);
    tempStitchSpeed=constrain(tempStitchSpeed, 1, 4);
    tempStitchScalar=constrain(tempStitchScalar, 1, 4);
    stitchAngle=90;
    gridClr=tempgridClr;
    sizeOfSquares=tempsizeOfSquares;
    boxPosX=tempBoxPosX;
    boxPosY=tempBoxPosY;
    stitchOffset=tempStitchOffset;
    stitchSpeed=tempStitchSpeed;
    stitchScalar= tempStitchScalar;
    stitchX=boxPosX+sizeOfSquares/2;
  } 


  // Method overloading for display function of four different stitch patterns

  // display () cross stitch

  void display (int stitchLength) {
    stroke(0);
    fill(gridClr);
    rect (boxPosX, boxPosY, sizeOfSquares, sizeOfSquares);

    for (float i=boxPosY; i<sizeOfSquares; i+=stitchLength) {      
      stroke(0);
      line (stitchX, i, stitchX+stitchLength, i+stitchLength);
      line (stitchX, i+stitchLength, stitchX+stitchLength, i);
    }
  }  // end the display () function



  // display () flat stitch

  void display (int stitchLength, float spacing) {
    stroke(0);
    fill(gridClr);
    rect (boxPosX, boxPosY, sizeOfSquares, sizeOfSquares);

    for (float i=boxPosY; i<sizeOfSquares; i+=stitchLength) {      

      stroke(0);
      line (stitchX, i, stitchX, sizeOfSquares);
      stroke (gridClr);
      line (stitchX, i+spacing, stitchX, sizeOfSquares);
    }
  }  // end the display () function


  // display () dotted stitch

  void display (int stitchLength, int dotSize) {
    stroke(0);
    fill(gridClr);
    rect (boxPosX, boxPosY, sizeOfSquares, sizeOfSquares);
    for (float i=boxPosY; i<sizeOfSquares; i+=stitchLength) {       // loop that will use a counter that will draw a shape every 8 pixels for the whole
      // height of the canvas
      stroke (strokeClr);       // determine the color of the stroke of the ellipses that form the dotted line as purple
      fill (clrLine);       // fill with purple the ellipses that form the dotted lines
      ellipse (stitchX, i, dotSize, dotSize);       // draw little ellipses every 8 pixels from top to bottom on the left of
      // the canvas to make up the dotted line
    }       // end the for loop
  }  // end the display () function


  // display () wavy stitch

  void display (float StitchOffset, float StitchSpeed, float StitchScalar) {
    stroke(0);
    fill(gridClr);
    rect (boxPosX, boxPosY, sizeOfSquares, sizeOfSquares);

    for (float i=boxPosY; i<sizeOfSquares; i+=stitchScalar) {    
      float waveStitch=stitchOffset+cos(radians(stitchAngle))*stitchScalar;
      stitchAngle+=stitchSpeed;
      stroke(0);
      strokeWeight (3);      
      fill (0);      
      point (stitchX+waveStitch, i);
    }       // end the for loop
   }  // end the display () function
}  // end Stitches class