You are an expert Verilog hardware designer working on a complete FPGA or ASIC project. You are given the full source code of a Verilog project. One of the modules in the project is incomplete — its implementation is missing and marked with:

// >>> Module Implementation Begin

// <<< Module Implementation End

Your task is to complete the missing implementation so that the entire project functions correctly. You must infer what the missing module or logic is supposed to do by analyzing the rest of the codebase: module names, signal connections, instantiations, comments, and usage patterns.

Follow these rules:

1. Only generate Verilog code to go between the `// >>> Module Implementation Begin` and `// <<< Module Implementation End` comments.
2. Use Verilog-2001 syntax. Ensure the code is synthesizable.
3. Assume the goal is a working, integrated hardware design — your code must make the whole system function as intended.
4. Analyze the naming, I/O ports, and how the module is instantiated or used in other parts of the project.
5. Implement correct behavior based on design context. Do not guess randomly — reason it out.
6. Avoid vendor-specific features unless explicitly required.
7. Do not output comments, explanation, or anything outside the required code region unless explicitly asked.

Your output should contain **only the Verilog code** that fits inside the marked region.

/*
 * Copyright (c) 2024 Rebecca G. Bettencourt
 * SPDX-License-Identifier: Apache-2.0
 */

`default_nettype none

module tt_um_rebeccargb_vga_timing_experiments (
    input  wire [7:0] ui_in,    // Dedicated inputs
    output wire [7:0] uo_out,   // Dedicated outputs
    input  wire [7:0] uio_in,   // IOs: Input path
    output wire [7:0] uio_out,  // IOs: Output path
    output wire [7:0] uio_oe,   // IOs: Enable path (active high: 0=input, 1=output)
    input  wire       ena,      // always 1 when the design is powered, so you can ignore it
    input  wire       clk,      // clock
    input  wire       rst_n     // reset_n - low to reset
);

  // VGA timing parameters
  reg [11:0] hdisplay;
  reg [9:0] hfrontporch;
  reg [9:0] hsynclength;
  reg [9:0] hbackporch;
  reg hsyncpolarity;
  reg [11:0] vdisplay;
  reg [7:0] vfrontporch;
  reg [7:0] vsynclength;
  reg [7:0] vbackporch;
  reg vsyncpolarity;

  // VGA signals
  wire hsync;
  wire vsync;
  wire display;
  wire [11:0] hpos;
  wire [11:0] vpos;
  wire [1:0] R;
  wire [1:0] G;
  wire [1:0] B;

  // TinyVGA PMOD
  assign uo_out = {hsync, B[0], G[0], R[0], vsync, B[1], G[1], R[1]};

  // Unused outputs assigned to 0.
  assign uio_out = 0;
  assign uio_oe  = 0;

  // Suppress unused signals warning
  wire _unused_ok = &{ena, ui_in, uio_in};

  hvsync_generator hvsync_gen(
    .hdisplay(hdisplay),
    .hfrontporch(hfrontporch),
    .hsynclength(hsynclength),
    .hbackporch(hbackporch),
    .hsyncpolarity(hsyncpolarity),
    .vdisplay(vdisplay),
    .vfrontporch(vfrontporch),
    .vsynclength(vsynclength),
    .vbackporch(vbackporch),
    .vsyncpolarity(vsyncpolarity),
    .clk(clk),
    .reset(~rst_n),
    .hsync(hsync),
    .vsync(vsync),
    .display(display),
    .hpos(hpos),
    .vpos(vpos)
  );

  reg [4:0] pattern;
  reg [5:0] color_in;
  wire [5:0] color_out;

  pattern_generator pat(
    .hpos(hpos),
    .vpos(vpos),
    .pattern(pattern),
    .color_in(color_in),
    .color_out(color_out)
  );

  assign R = display ? color_out[5:4] : 2'b00;
  assign G = display ? color_out[3:2] : 2'b00;
  assign B = display ? color_out[1:0] : 2'b00;

  always @(posedge ui_in[7])
  begin
    case (ui_in[3:0])
      4'd0: begin
        hdisplay <= 640;
        hfrontporch <= 16;
        hsynclength <= 96;
        hbackporch <= 48;
        hsyncpolarity <= 0;
        vdisplay <= 480;
        vfrontporch <= 10;
        vsynclength <= 2;
        vbackporch <= 33;
        vsyncpolarity <= 0;
        pattern <= 5'd31;
        color_in <= 0;
      end
      4'd1: pattern <= pattern + 1;
      4'd2: pattern <= pattern - 1;
      4'd3: pattern <= uio_in[4:0];
      4'd4: hdisplay <= {1'b0, ui_in[6:4], uio_in};
      4'd5: hfrontporch <= {ui_in[5:4], uio_in};
      4'd6: {hsyncpolarity, hsynclength} <= {ui_in[6], ui_in[5:4], uio_in};
      4'd7: hbackporch <= {ui_in[5:4], uio_in};
      4'd8: vdisplay <= {1'b0, ui_in[6:4], uio_in};
      4'd9: vfrontporch <= uio_in;
      4'd10: {vsyncpolarity, vsynclength} <= {ui_in[6], uio_in};
      4'd11: vbackporch <= uio_in;
      4'd12: color_in <= uio_in[5:0];
      4'd13: color_in <= color_in + 1;
      4'd14: color_in <= color_in - 1;
      4'd15: begin
        hdisplay <= 640;
        hfrontporch <= 16;
        hsynclength <= 96;
        hbackporch <= 48;
        hsyncpolarity <= 0;
        vdisplay <= 480;
        vfrontporch <= 10;
        vsynclength <= 2;
        vbackporch <= 33;
        vsyncpolarity <= 0;
        pattern <= 5'd31;
        color_in <= 0;
      end
    endcase
  end

endmodule


module hvsync_generator(
	input wire [11:0] hdisplay,
	input wire [9:0] hfrontporch,
	input wire [9:0] hsynclength,
	input wire [9:0] hbackporch,
	input wire hsyncpolarity,
	input wire [11:0] vdisplay,
	input wire [7:0] vfrontporch,
	input wire [7:0] vsynclength,
	input wire [7:0] vbackporch,
	input wire vsyncpolarity,
	input wire clk,
	input wire reset,
	output reg hsync,
	output reg vsync,
	output wire display,
	output reg [11:0] hpos,
	output reg [11:0] vpos
);

	wire [11:0] hsyncstart = hdisplay + hfrontporch;
	wire [11:0] hsyncend = hdisplay + hfrontporch + hsynclength - 1;
	wire [11:0] hmax = hdisplay + hbackporch + hfrontporch + hsynclength - 1;
	wire [11:0] vsyncstart = vdisplay + vfrontporch;
	wire [11:0] vsyncend = vdisplay + vfrontporch + vsynclength - 1;
	wire [11:0] vmax = vdisplay + vbackporch + vfrontporch + vsynclength - 1;

	wire hmaxxed = (hpos == hmax) || reset;
	wire vmaxxed = (vpos == vmax) || reset;

	always @(posedge clk)
	begin
		hsync <= (hpos >= hsyncstart && hpos <= hsyncend) ^ hsyncpolarity;
		if (hmaxxed) hpos <= 0;
		else hpos <= hpos + 1;
	end

	always @(posedge clk)
	begin
		vsync <= (vpos >= vsyncstart && vpos <= vsyncend) ^ vsyncpolarity;
		if (hmaxxed) begin
			if (vmaxxed) vpos <= 0;
			else vpos <= vpos + 1;
		end
	end

	assign display = (hpos < hdisplay) && (vpos < vdisplay);

endmodule


module pattern_generator(
	input wire [11:0] hpos,
	input wire [11:0] vpos,
	input wire [4:0] pattern,
	input wire [5:0] color_in,
	output reg [5:0] color_out
);
// >>> Module Implementation Begin

// <<< Module Implementation End
endmodule




Reference solution:
rtl/generated.v: 
	always @(*)
	begin
		case (pattern)
			5'd0: color_out = color_in; // solid color

			5'd1: color_out = (hpos[0] ^ vpos[0]) ? (color_in ^ 6'b111111) : color_in; // 1x1 checker
			5'd2: color_out = (hpos[1] ^ vpos[1]) ? (color_in ^ 6'b111111) : color_in; // 2x2 checker
			5'd3: color_out = (hpos[2] ^ vpos[2]) ? (color_in ^ 6'b111111) : color_in; // 4x4 checker
			5'd4: color_out = (hpos[3] ^ vpos[3]) ? (color_in ^ 6'b111111) : color_in; // 8x8 checker
			5'd5: color_out = (hpos[4] ^ vpos[4]) ? (color_in ^ 6'b111111) : color_in; // 16x16 checker
			5'd6: color_out = (hpos[5] ^ vpos[5]) ? (color_in ^ 6'b111111) : color_in; // 32x32 checker
			5'd7: color_out = (hpos[6] ^ vpos[6]) ? (color_in ^ 6'b111111) : color_in; // 64x64 checker

			5'd8: color_out = (hpos[2:0] == 0 || hpos[2:0] == 3'b111 || vpos[2:0] == 0 || vpos[2:0] == 3'b111) ? (color_in ^ 6'b111111) : color_in; // 8x8 grid
			5'd9: color_out = (hpos[3:0] == 0 || hpos[3:0] == 4'b1111 || vpos[3:0] == 0 || vpos[3:0] == 4'b1111) ? (color_in ^ 6'b111111) : color_in; // 16x16 grid
			5'd10: color_out = (hpos[4:0] == 0 || hpos[4:0] == 5'b11111 || vpos[4:0] == 0 || vpos[4:0] == 5'b11111) ? (color_in ^ 6'b111111) : color_in; // 32x32 grid
			5'd11: color_out = (hpos[5:0] == 0 || hpos[5:0] == 6'b111111 || vpos[5:0] == 0 || vpos[5:0] == 6'b111111) ? (color_in ^ 6'b111111) : color_in; // 64x64 grid

			5'd12: color_out = {vpos[2], hpos[2], vpos[1:0], hpos[1:0]}; // 1x1 color blocks
			5'd13: color_out = {vpos[3], hpos[3], vpos[2:1], hpos[2:1]}; // 2x2 color blocks
			5'd14: color_out = {vpos[4], hpos[4], vpos[3:2], hpos[3:2]}; // 4x4 color blocks
			5'd15: color_out = {vpos[5], hpos[5], vpos[4:3], hpos[4:3]}; // 8x8 color blocks
			5'd16: color_out = {vpos[6], hpos[6], vpos[5:4], hpos[5:4]}; // 16x16 color blocks
			5'd17: color_out = {vpos[7], hpos[7], vpos[6:5], hpos[6:5]}; // 32x32 color blocks

			5'd18: color_out = hpos[5:0] + vpos[5:0]; // 1x1 color blocks
			5'd19: color_out = hpos[6:1] + vpos[6:1]; // 2x2 color blocks
			5'd20: color_out = hpos[7:2] + vpos[7:2]; // 4x4 color blocks
			5'd21: color_out = hpos[8:3] + vpos[8:3]; // 8x8 color blocks
			5'd22: color_out = hpos[9:4] + vpos[9:4]; // 16x16 color blocks
			5'd23: color_out = hpos[10:5] + vpos[10:5]; // 32x32 color blocks

			5'd24: color_out = hpos[5:0] - vpos[5:0]; // 1x1 color blocks
			5'd25: color_out = hpos[6:1] - vpos[6:1]; // 2x2 color blocks
			5'd26: color_out = hpos[7:2] - vpos[7:2]; // 4x4 color blocks
			5'd27: color_out = hpos[8:3] - vpos[8:3]; // 8x8 color blocks
			5'd28: color_out = hpos[9:4] - vpos[9:4]; // 16x16 color blocks
			5'd29: color_out = hpos[10:5] - vpos[10:5]; // 32x32 color blocks

			5'd30: color_out = {~vpos[6], ~vpos[6], ~vpos[7], ~vpos[7], ~vpos[5], ~vpos[5]}; // horizontal color bars
			5'd31: color_out = {~hpos[6], ~hpos[6], ~hpos[7], ~hpos[7], ~hpos[5], ~hpos[5]}; // vertical color bars
		endcase
	end