A simple activity with a drawing view and a rainbow brush. Proof of concept. Potential to be improved.

Rainbow_Brush_Demo

import android.app.Activity;
import android.graphics.Bitmap;
import android.graphics.Canvas;
import android.graphics.Color;
import android.graphics.Paint;
import android.graphics.Path;
import android.os.Bundle;
import android.support.v7.app.ActionBarActivity;
import android.view.MotionEvent;
import android.view.View;

import java.util.ArrayList;
import java.util.List;
import java.util.Random;


public class MainActivity extends ActionBarActivity {

    DrawingView mDrawingView;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        mDrawingView = new DrawingView(this);
        setContentView(mDrawingView);
    }

    public class DrawingView extends View {

        public int width;
        public int height;

        private Bitmap mBitmap;
        private Canvas mCanvas;

        private Paint mBitmapPaint;

        private Paint mCirclePaint;
        private Path mCirclePath;

        private Paint mLinePaint;
        private Path mLinePath;

        private float mX, mY;
        private static final float TOUCH_TOLERANCE = 10;
        private int mCurrentColorIndex = 0;
        private static final int BRUSH_RADIUS = 30;

        private final List<Integer> mColoursList;

        public DrawingView(Activity c) {
            super(c);

            mColoursList = initRainbowColors();

            mBitmapPaint = new Paint(Paint.DITHER_FLAG);

            mCirclePath = new Path();
            mCirclePaint = new Paint();
            mCirclePaint.setAntiAlias(true);
            mCirclePaint.setDither(true);
            mCirclePaint.setColor(getColorIndex());
            mCirclePaint.setStyle(Paint.Style.FILL);
            mCirclePaint.setStrokeJoin(Paint.Join.ROUND);

            mLinePath = new Path();
            mLinePaint = new Paint();
            mLinePaint.setAntiAlias(true);
            mLinePaint.setDither(true);
            mLinePaint.setColor(getColorIndex());
            mLinePaint.setStyle(Paint.Style.STROKE);
            mLinePaint.setStrokeJoin(Paint.Join.ROUND);
            mLinePaint.setStrokeCap(Paint.Cap.ROUND);
            mLinePaint.setStrokeWidth(BRUSH_RADIUS * 2);

        }

        private List<Integer> initRainbowColors(){
            final List<Integer> colorsList = new ArrayList<>();
            for (int r = 0; r < 100; r++) colorsList.add(Color.rgb(r * 255 / 100, 255, 0));
            for (int g = 100; g > 0; g--) colorsList.add(Color.rgb(255, g * 255 / 100, 0));
            for (int b = 0; b < 100; b++) colorsList.add(Color.rgb(255, 0, b * 255 / 100));
            for (int r = 100; r > 0; r--) colorsList.add(Color.rgb(r * 255 / 100, 0, 255));
            for (int g = 0; g < 100; g++) colorsList.add(Color.rgb(0, g * 255 / 100, 255));
            for (int b = 100; b > 0; b--) colorsList.add(Color.rgb(0, 255, b * 255 / 100));
            colorsList.add(Color.rgb(0, 255, 0));
            return colorsList;
        }

        @Override
        protected void onSizeChanged(int w, int h, int oldw, int oldh) {
            super.onSizeChanged(w, h, oldw, oldh);
            mBitmap = Bitmap.createBitmap(w, h, Bitmap.Config.ARGB_8888);
            mCanvas = new Canvas(mBitmap);
        }

        @Override
        protected void onDraw(Canvas canvas) {
            super.onDraw(canvas);
            canvas.drawBitmap(mBitmap, 0, 0, mBitmapPaint);
            canvas.drawPath(mCirclePath, mCirclePaint);
            canvas.drawPath(mLinePath, mLinePaint);
        }


        private void touchStart(float x, float y) {
            mLinePath.reset();
            mLinePath.moveTo(x, y);
            mX = x;
            mY = y;
        }

        private void touchMove(float x, float y) {

            float dx = Math.abs(x - mX);
            float dy = Math.abs(y - mY);

            mLinePath.reset();
            mLinePath.moveTo(x, y);

            if (dx >= TOUCH_TOLERANCE || dy >= TOUCH_TOLERANCE) {

                mLinePath.quadTo(mX, mY, (x + mX) / 2, (y + mY) / 2);
                mCanvas.drawPath(mLinePath, mLinePaint); // draw to canvas each move

                mCirclePath.reset();
                mCirclePath.addCircle(mX, mY, BRUSH_RADIUS, Path.Direction.CW);
                mCanvas.drawPath(mCirclePath, mCirclePaint); // draw to canvas each move

                mX = x;
                mY = y;

            }
        }

        private void touchUp() {
            mLinePath.lineTo(mX, mY);
            mCirclePath.reset();
            // commit the path to our offscreen
            mCanvas.drawPath(mLinePath, mLinePaint);
            // kill this so we don't double draw
            mLinePath.reset();
        }

        final Random r = new Random();

        @Override
        public boolean onTouchEvent(MotionEvent event) {

            float x = event.getX();
            float y = event.getY();

            switch (event.getAction()) {
                case MotionEvent.ACTION_DOWN:
                    touchStart(x, y);
                    invalidate();
                    break;
                case MotionEvent.ACTION_MOVE:
                    touchMove(x, y);
                    mLinePaint.setColor(mColoursList.get(getColorIndex()));
                    mCirclePaint.setColor(mColoursList.get(getColorIndex()));
                    invalidate();
                    break;
                case MotionEvent.ACTION_UP:
                    touchUp();
                    invalidate();
                    break;
            }
            return true;
        }

        private int getColorIndex(){
            int size = mColoursList.size();
            if(mCurrentColorIndex == size){
                mCurrentColorIndex = 0;
            }
            return mCurrentColorIndex++;
        }
    }
}