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 James Ross
 * SPDX-License-Identifier: Apache-2.0
 */

`default_nettype none

module tt_um_nvious_graphics(
	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 signals
	wire hsync;
	wire vsync;
	wire [5:0] RGB;
	wire video_active;
	wire [9:0] x;
	wire [9:0] y;

	// TinyVGA PMOD
	assign uo_out = {hsync, RGB[0], RGB[2], RGB[4], vsync, RGB[1], RGB[3], RGB[5]};

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

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

	reg show;
	reg [9:0] counter;
	wire [7:0] led = show ? ui_in : countdown[counter[9:6]];

	reg [7:0] countdown[15:0];
	initial begin
		countdown[ 0] = 8'b01100111; // 9
		countdown[ 1] = 8'b01111111; // 8
		countdown[ 2] = 8'b00000111; // 7
		countdown[ 3] = 8'b01111101; // 6
		countdown[ 4] = 8'b01101101; // 5
		countdown[ 5] = 8'b01100110; // 4
		countdown[ 6] = 8'b01001111; // 3
		countdown[ 7] = 8'b01011011; // 2
		countdown[ 8] = 8'b00000110; // 1
		countdown[ 9] = 8'b00111111; // 0
		countdown[10] = 8'b10000000; // .
		countdown[11] = 8'b00000000; // 
		countdown[12] = 8'b10000000; // .
		countdown[13] = 8'b00000000; // 
		countdown[14] = 8'b10000000; // .
		countdown[15] = 8'b00000000; // 
	end

	// VGA output
	hvsync_generator hvsync_gen(
		.clk(clk),
		.reset(~rst_n),
		.hsync(hsync),
		.vsync(vsync),
		.display_on(video_active),
		.hpos(x),
		.vpos(y)
	);

	// gradient
	wire gsky; // gradient sky
	gradient_rom gradient_sky(
		.y(y[6:0]),
		.x(x[1:0]),
		.pixel(gsky)
	);

	wire gsun; // gradient of sun
	gradient_rom gradient_sun(
		.y(sy1[6:0]),
		.x(x[1:0]),
		.pixel(gsun)
	);

	wire a0 = y > 7;
	wire a1 = x < y + 392;
	wire a2 = 454 - x > y;
	wire a3 = y < 56;
	wire a4 = x > y + 185;
	wire a5 = x > 247 - y;
	wire a = a0 & a1 & a2 & a3 & a4 & a5;

	wire b0 = a1;
	wire b1 = x < 448;
	wire b2 = 662 - x > y;
	wire b3 = a4;
	wire b4 = x > 399;
	wire b5 = 455 - x < y;
	wire b = b0 & b1 & b2 & b3 & b4 & b5;

	wire c0 = x < y + 184;
	wire c1 = b1;
	wire c2 = 872 - x > y;
	wire c3 = x + 23 > y;
	wire c4 = b4;
	wire c5 = 663 - x < y;
	wire c = c0 & c1 & c2 & c3 & c4 & c5;

	wire d0 = y > 423;
	wire d1 = y > x + 24; 
	wire d2 = c2;
	wire d3 = y < 472;
	wire d4 = x > y - 232;
	wire d5 = c5;
	wire d = d0 & d1 & d2 & d3 & d4 & d5;

	wire e0 = d1;
	wire e1 = x < 240;
	wire e2 = b2;
	wire e3 = d4;
	wire e4 = x > 191;
	wire e5 = b5;
	wire e = e0 & e1 & e2 & e3 & e4 & e5;

	wire f0 = c0;
	wire f1 = e1;
	wire f2 = a2;
	wire f3 = c3;
	wire f4 = e4;
	wire f5 = a5;
	wire f = f0 & f1 & f2 & f3 & f4 & f5;

	wire g0 = y > 215;
	wire g1 = c0;
	wire g2 = b2;
	wire g3 = y < 262;
	wire g4 = f3;
	wire g5 = e5;
	wire g = g0 & g1 & g2 & g3 & g4 & g5;

	wire [9:0] hx0 = x - 511;
	wire [9:0] hy0 = 439 - y;
	wire [9:0] hx1 = 512 - x;
	wire [9:0] hy1 = y - 440;
	wire hq0 = (hy0[4:0] < (circle[{hx0[4:0],2'b00}][6:2])) & (hx0 < 32) & (hy0 < 32);
	wire hq1 = (hy0[4:0] < (circle[{hx1[4:0],2'b00}][6:2])) & (hx1 < 32) & (hy0 < 32);
	wire hq2 = (hy1[4:0] < (circle[{hx0[4:0],2'b00}][6:2])) & (hx0 < 32) & (hy1 < 32);
	wire hq3 = (hy1[4:0] < (circle[{hx1[4:0],2'b00}][6:2])) & (hx1 < 32) & (hy1 < 32);
	wire h = hq0 | hq1 | hq2 | hq3;

	wire [9:0] sx0 = x - 320;
	wire [9:0] sy0 = 239 - y;
	wire [9:0] sx1 = 319 - x;
	wire [9:0] sy1 = y - 240;
	wire sq0 = (sy0[6:0] < (circle[sx0[6:0]])) & (sx0 < 128) & (sy0 < 128);
	wire sq1 = (sy0[6:0] < (circle[sx1[6:0]])) & (sx1 < 128) & (sy0 < 128);
	wire sq2 = (sy1[6:0] < (circle[sx0[6:0]])) & (sx0 < 128) & (sy1 < 64);
	wire sq3 = (sy1[6:0] < (circle[sx1[6:0]])) & (sx1 < 128) & (sy1 < 64);
	wire s = sq0 | sq1 | sq2 | sq3;

	wire ey0 = y == 10'd304;
	wire ey1 = (y > 10'd304) & (y == 10'd305 + {9'd0, counter[6]});
	wire ey2 = (y > 10'd306) & (y == 10'd307 + {8'd0, counter[6:5]});
	wire ey3 = (y > 10'd310) & (y == 10'd311 + {7'd0, counter[6:4]});
	wire ey4 = (y > 10'd318) & (y == 10'd319 + {6'd0, counter[6:3]});
	wire ey5 = (y > 10'd334) & (y == 10'd335 + {5'd0, counter[6:2]});
	wire ey6 = (y > 10'd366) & (y == 10'd367 + {4'd0, counter[6:1]});
	wire ey7 = (y > 10'd430) & (y == 10'd431 + {3'd0, counter[6:0]});
	wire ey = ey0 | ey1 | ey2 | ey3 | ey4 | ey5 | ey6 | ey7;
	wire ex0 = x == 320;
	wire ex1 = y == x - 80;
	wire ex2 = y == 559 - x;
	wire ex3 = y == (x>>1) + 80;
	wire ex4 = y == 399 - (x>>1);
	wire ex5 = y == (x>>2) + (x>>4) + 141;
	wire ex6 = y == 339 - (x>>2) - (x>>4);
	wire ex = (y > 10'd304) & (ex0 | ex1 | ex2 | ex3 | ex4 | ex5 | ex6);

	wire [5:0] black  = 6'b000000;
	wire [5:0] star   = 6'b001011;
	wire [5:0] cyan   = 6'b001111;
	wire [5:0] red    = 6'b110001;
	wire [5:0] orange = 6'b110101;
	wire [5:0] yellow = 6'b111101;
	wire [5:0] pink   = 6'b110111;
	wire [5:0] purple = 6'b100010;
	wire [5:0] blue   = 6'b000001;

	// background (sky)
	wire [5:0] bg = (y < 128) ? (gsky ? blue : black) : ((y > 200 && sy1 < 64) ? (gsun ? purple : blue) : (y > sy1) ? black: blue);
	// c-ground (stars)
	wire [5:0] cg = ((x[6]^y[6]) & (x[5:0]==32 & y[5:0]==32) & (y < sy1) ) ? star : bg;
	// d-ground (sun)
	wire [5:0] dg = s ? ((sy1 < 128) ? (gsun ? red : orange) : (gsun ? orange : yellow)) : cg;
	// e-ground
	wire [5:0] eg = ex | ey ? pink : dg;
	// foreground
	wire [5:0] fg = cyan;
	assign RGB = video_active ? (((a & led[0]) | (b & led[1]) | (c & led[2]) | (d & led[3]) | (e & led[4]) | (f & led[5]) | (g & led[6]) | (h & led[7])) ? fg : eg) : black;

	always @(posedge vsync) begin
		if (~rst_n) begin
			show <= 0;
			counter <= 0;
		end else begin
			show <= show | ui_in[0] | ui_in[1] | ui_in[2] | ui_in[3] | ui_in[4] | ui_in[5] | ui_in[6] | ui_in[7];
			counter <= counter + 1;
		end
	end

	reg [6:0] circle[0:127];
	initial begin
		circle[  0] = 7'd127;
		circle[  1] = 7'd127;
		circle[  2] = 7'd127;
		circle[  3] = 7'd127;
		circle[  4] = 7'd127;
		circle[  5] = 7'd127;
		circle[  6] = 7'd127;
		circle[  7] = 7'd127;
		circle[  8] = 7'd127;
		circle[  9] = 7'd127;
		circle[ 10] = 7'd127;
		circle[ 11] = 7'd127;
		circle[ 12] = 7'd127;
		circle[ 13] = 7'd127;
		circle[ 14] = 7'd127;
		circle[ 15] = 7'd126;
		circle[ 16] = 7'd126;
		circle[ 17] = 7'd126;
		circle[ 18] = 7'd126;
		circle[ 19] = 7'd126;
		circle[ 20] = 7'd126;
		circle[ 21] = 7'd126;
		circle[ 22] = 7'd125;
		circle[ 23] = 7'd125;
		circle[ 24] = 7'd125;
		circle[ 25] = 7'd125;
		circle[ 26] = 7'd125;
		circle[ 27] = 7'd124;
		circle[ 28] = 7'd124;
		circle[ 29] = 7'd124;
		circle[ 30] = 7'd124;
		circle[ 31] = 7'd123;
		circle[ 32] = 7'd123;
		circle[ 33] = 7'd123;
		circle[ 34] = 7'd123;
		circle[ 35] = 7'd122;
		circle[ 36] = 7'd122;
		circle[ 37] = 7'd122;
		circle[ 38] = 7'd121;
		circle[ 39] = 7'd121;
		circle[ 40] = 7'd121;
		circle[ 41] = 7'd120;
		circle[ 42] = 7'd120;
		circle[ 43] = 7'd120;
		circle[ 44] = 7'd119;
		circle[ 45] = 7'd119;
		circle[ 46] = 7'd119;
		circle[ 47] = 7'd118;
		circle[ 48] = 7'd118;
		circle[ 49] = 7'd117;
		circle[ 50] = 7'd117;
		circle[ 51] = 7'd116;
		circle[ 52] = 7'd116;
		circle[ 53] = 7'd116;
		circle[ 54] = 7'd115;
		circle[ 55] = 7'd115;
		circle[ 56] = 7'd114;
		circle[ 57] = 7'd114;
		circle[ 58] = 7'd113;
		circle[ 59] = 7'd113;
		circle[ 60] = 7'd112;
		circle[ 61] = 7'd111;
		circle[ 62] = 7'd111;
		circle[ 63] = 7'd110;
		circle[ 64] = 7'd110;
		circle[ 65] = 7'd109;
		circle[ 66] = 7'd109;
		circle[ 67] = 7'd108;
		circle[ 68] = 7'd107;
		circle[ 69] = 7'd107;
		circle[ 70] = 7'd106;
		circle[ 71] = 7'd105;
		circle[ 72] = 7'd105;
		circle[ 73] = 7'd104;
		circle[ 74] = 7'd103;
		circle[ 75] = 7'd102;
		circle[ 76] = 7'd102;
		circle[ 77] = 7'd101;
		circle[ 78] = 7'd100;
		circle[ 79] = 7'd99;
		circle[ 80] = 7'd99;
		circle[ 81] = 7'd98;
		circle[ 82] = 7'd97;
		circle[ 83] = 7'd96;
		circle[ 84] = 7'd95;
		circle[ 85] = 7'd94;
		circle[ 86] = 7'd93;
		circle[ 87] = 7'd92;
		circle[ 88] = 7'd91;
		circle[ 89] = 7'd91;
		circle[ 90] = 7'd90;
		circle[ 91] = 7'd88;
		circle[ 92] = 7'd87;
		circle[ 93] = 7'd86;
		circle[ 94] = 7'd85;
		circle[ 95] = 7'd84;
		circle[ 96] = 7'd83;
		circle[ 97] = 7'd82;
		circle[ 98] = 7'd81;
		circle[ 99] = 7'd79;
		circle[100] = 7'd78;
		circle[101] = 7'd77;
		circle[102] = 7'd75;
		circle[103] = 7'd74;
		circle[104] = 7'd73;
		circle[105] = 7'd71;
		circle[106] = 7'd70;
		circle[107] = 7'd68;
		circle[108] = 7'd67;
		circle[109] = 7'd65;
		circle[110] = 7'd63;
		circle[111] = 7'd61;
		circle[112] = 7'd60;
		circle[113] = 7'd58;
		circle[114] = 7'd56;
		circle[115] = 7'd54;
		circle[116] = 7'd51;
		circle[117] = 7'd49;
		circle[118] = 7'd47;
		circle[119] = 7'd44;
		circle[120] = 7'd41;
		circle[121] = 7'd38;
		circle[122] = 7'd35;
		circle[123] = 7'd31;
		circle[124] = 7'd27;
		circle[125] = 7'd22;
		circle[126] = 7'd15;
		circle[127] = 7'd0;
	end
endmodule


`ifndef GRADIENT_ROM_H
`define GRADIENT_ROM_H

// Gradient lookup table

module gradient_rom(
	input wire [6:0] y,
	input wire [1:0] x,
	output wire pixel
);
// >>> Module Implementation Begin

// <<< Module Implementation End
endmodule



`endif


`ifndef HVSYNC_GENERATOR_H
`define HVSYNC_GENERATOR_H

/*
Video sync generator, used to drive a VGA monitor.
Timing from: https://en.wikipedia.org/wiki/Video_Graphics_Array
To use:
- Wire the hsync and vsync signals to top level outputs
- Add a 3-bit (or more) "rgb" output to the top level
*/

module hvsync_generator(clk, reset, hsync, vsync, display_on, hpos, vpos);

  input clk;
  input reset;
  output reg hsync, vsync;
  output display_on;
  output reg [9:0] hpos;
  output reg [9:0] vpos;

  // declarations for TV-simulator sync parameters
  // horizontal constants
  parameter H_DISPLAY       = 640; // horizontal display width
  parameter H_BACK          =  48; // horizontal left border (back porch)
  parameter H_FRONT         =  16; // horizontal right border (front porch)
  parameter H_SYNC          =  96; // horizontal sync width
  // vertical constants
  parameter V_DISPLAY       = 480; // vertical display height
  parameter V_TOP           =  33; // vertical top border
  parameter V_BOTTOM        =  10; // vertical bottom border
  parameter V_SYNC          =   2; // vertical sync # lines
  // derived constants
  parameter H_SYNC_START    = H_DISPLAY + H_FRONT;
  parameter H_SYNC_END      = H_DISPLAY + H_FRONT + H_SYNC - 1;
  parameter H_MAX           = H_DISPLAY + H_BACK + H_FRONT + H_SYNC - 1;
  parameter V_SYNC_START    = V_DISPLAY + V_BOTTOM;
  parameter V_SYNC_END      = V_DISPLAY + V_BOTTOM + V_SYNC - 1;
  parameter V_MAX           = V_DISPLAY + V_TOP + V_BOTTOM + V_SYNC - 1;

  wire hmaxxed = (hpos == H_MAX) || reset;	// set when hpos is maximum
  wire vmaxxed = (vpos == V_MAX) || reset;	// set when vpos is maximum
  
  // horizontal position counter
  always @(posedge clk)
  begin
    hsync <= (hpos>=H_SYNC_START && hpos<=H_SYNC_END);
    if(hmaxxed)
      hpos <= 0;
    else
      hpos <= hpos + 1;
  end

  // vertical position counter
  always @(posedge clk)
  begin
    vsync <= (vpos>=V_SYNC_START && vpos<=V_SYNC_END);
    if(hmaxxed)
      if (vmaxxed)
        vpos <= 0;
      else
        vpos <= vpos + 1;
  end
  
  // display_on is set when beam is in "safe" visible frame
  assign display_on = (hpos<H_DISPLAY) && (vpos<V_DISPLAY);

endmodule

`endif


Reference solution:
rtl/generated.v: 	reg [3:0] g[127:0];
	assign pixel = g[y][x];

	initial begin
		g[  0] = 4'b0000;
		g[  1] = 4'b0000;
		g[  2] = 4'b0000;
		g[  3] = 4'b0000;
		g[  4] = 4'b0100;
		g[  5] = 4'b0000;
		g[  6] = 4'b0000;
		g[  7] = 4'b0000;
		g[  8] = 4'b0100;
		g[  9] = 4'b0000;
		g[ 10] = 4'b0001;
		g[ 11] = 4'b0000;
		g[ 12] = 4'b0100;
		g[ 13] = 4'b0000;
		g[ 14] = 4'b0001;
		g[ 15] = 4'b0000;
		g[ 16] = 4'b0100;
		g[ 17] = 4'b0000;
		g[ 18] = 4'b0101;
		g[ 19] = 4'b0000;
		g[ 20] = 4'b0100;
		g[ 21] = 4'b0000;
		g[ 22] = 4'b0101;
		g[ 23] = 4'b0000;
		g[ 24] = 4'b0100;
		g[ 25] = 4'b0000;
		g[ 26] = 4'b0101;
		g[ 27] = 4'b0000;
		g[ 28] = 4'b0101;
		g[ 29] = 4'b0000;
		g[ 30] = 4'b0101;
		g[ 31] = 4'b0000;
		g[ 32] = 4'b0101;
		g[ 33] = 4'b0000;
		g[ 34] = 4'b0101;
		g[ 35] = 4'b0010;
		g[ 36] = 4'b0101;
		g[ 37] = 4'b0000;
		g[ 38] = 4'b0101;
		g[ 39] = 4'b0010;
		g[ 40] = 4'b0101;
		g[ 41] = 4'b1000;
		g[ 42] = 4'b0101;
		g[ 43] = 4'b0010;
		g[ 44] = 4'b0101;
		g[ 45] = 4'b1000;
		g[ 46] = 4'b0101;
		g[ 47] = 4'b0010;
		g[ 48] = 4'b0101;
		g[ 49] = 4'b1010;
		g[ 50] = 4'b0101;
		g[ 51] = 4'b0010;
		g[ 52] = 4'b0101;
		g[ 53] = 4'b1010;
		g[ 54] = 4'b0101;
		g[ 55] = 4'b0010;
		g[ 56] = 4'b0101;
		g[ 57] = 4'b1010;
		g[ 58] = 4'b0101;
		g[ 59] = 4'b1010;
		g[ 60] = 4'b0101;
		g[ 61] = 4'b1010;
		g[ 62] = 4'b0101;
		g[ 63] = 4'b1010;
		g[ 64] = 4'b0101;
		g[ 65] = 4'b1010;
		g[ 66] = 4'b0101;
		g[ 67] = 4'b1110;
		g[ 68] = 4'b0101;
		g[ 69] = 4'b1010;
		g[ 70] = 4'b0101;
		g[ 71] = 4'b1110;
		g[ 72] = 4'b0101;
		g[ 73] = 4'b1011;
		g[ 74] = 4'b0101;
		g[ 75] = 4'b1110;
		g[ 76] = 4'b0101;
		g[ 77] = 4'b1011;
		g[ 78] = 4'b0101;
		g[ 79] = 4'b1110;
		g[ 80] = 4'b0101;
		g[ 81] = 4'b1111;
		g[ 82] = 4'b0101;
		g[ 83] = 4'b1110;
		g[ 84] = 4'b0101;
		g[ 85] = 4'b1111;
		g[ 86] = 4'b0101;
		g[ 87] = 4'b1110;
		g[ 88] = 4'b0101;
		g[ 89] = 4'b1111;
		g[ 90] = 4'b0101;
		g[ 91] = 4'b1111;
		g[ 92] = 4'b0101;
		g[ 93] = 4'b1111;
		g[ 94] = 4'b0101;
		g[ 95] = 4'b1111;
		g[ 96] = 4'b0101;
		g[ 97] = 4'b1111;
		g[ 98] = 4'b0101;
		g[ 99] = 4'b1111;
		g[100] = 4'b0111;
		g[101] = 4'b1111;
		g[102] = 4'b0101;
		g[103] = 4'b1111;
		g[104] = 4'b0111;
		g[105] = 4'b1111;
		g[106] = 4'b1101;
		g[107] = 4'b1111;
		g[108] = 4'b0111;
		g[109] = 4'b1111;
		g[110] = 4'b1101;
		g[111] = 4'b1111;
		g[112] = 4'b0111;
		g[113] = 4'b1111;
		g[114] = 4'b1111;
		g[115] = 4'b1111;
		g[116] = 4'b0111;
		g[117] = 4'b1111;
		g[118] = 4'b1111;
		g[119] = 4'b1111;
		g[120] = 4'b0111;
		g[121] = 4'b1111;
		g[122] = 4'b1111;
		g[123] = 4'b1111;
		g[124] = 4'b1111;
		g[125] = 4'b1111;
		g[126] = 4'b1111;
		g[127] = 4'b1111;
	end