diff --git a/TODO.md b/TODO.md
index 6c197ca..c8cd9d3 100644
--- a/TODO.md
+++ b/TODO.md
@@ -9,15 +9,15 @@
 
 ## phase 2: single-player simulation
 
-- [ ] define GameState, Player, Projectile structs
-- [ ] terrain generation (random jagged line)
-- [ ] cannon aiming (angle adjustment with keys)
-- [ ] power adjustment
-- [ ] fire projectile
-- [ ] projectile physics (gravity, movement)
-- [ ] terrain collision detection
-- [ ] player hit detection
-- [ ] turn switching after shot resolves
+- [x] define GameState, Player, Projectile structs
+- [x] terrain generation (fixed pattern for now)
+- [x] cannon aiming (angle adjustment with keys)
+- [x] power adjustment
+- [x] fire projectile
+- [x] projectile physics (gravity, movement)
+- [x] terrain collision detection
+- [x] player hit detection
+- [x] turn switching after shot resolves
 
 ## phase 3: rendering
 
diff --git a/src/game.zig b/src/game.zig
new file mode 100644
index 0000000..cab15e6
--- /dev/null
+++ b/src/game.zig
@@ -0,0 +1,241 @@
+// game state and simulation
+// fully deterministic - no floats, no hashmaps, no system time
+
+const std = @import("std");
+const Fixed = @import("fixed.zig").Fixed;
+const trig = @import("trig.zig");
+const Terrain = @import("terrain.zig").Terrain;
+const SCREEN_WIDTH = @import("terrain.zig").SCREEN_WIDTH;
+
+// simulation constants
+const ANGLE_SPEED: Fixed = Fixed.fromFloat(0.02); // radians per tick when adjusting
+const POWER_SPEED: Fixed = Fixed.ONE; // units per tick when adjusting
+const MIN_ANGLE: Fixed = Fixed.ZERO;
+const MAX_ANGLE: Fixed = Fixed.PI;
+const MIN_POWER: Fixed = Fixed.ZERO;
+const MAX_POWER: Fixed = Fixed.fromInt(100);
+const DAMAGE: i32 = 50;
+const HIT_RADIUS: Fixed = Fixed.fromInt(20);
+const PROJECTILE_SPEED_FACTOR: Fixed = Fixed.fromFloat(0.15);
+
+pub const Player = struct {
+    x: Fixed,
+    y: Fixed, // sits on terrain
+    cannon_angle: Fixed, // radians, 0 to PI (0=right, PI=left)
+    power: Fixed, // 0 to 100
+    health: i32,
+    alive: bool,
+};
+
+pub const Projectile = struct {
+    x: Fixed,
+    y: Fixed,
+    vx: Fixed,
+    vy: Fixed,
+};
+
+pub const GameState = struct {
+    tick: u32,
+    current_turn: u8, // 0 or 1
+    wind: Fixed,
+    players: [2]Player,
+    projectile: ?Projectile,
+    terrain: *const Terrain,
+    rng_state: u64,
+};
+
+pub const Input = struct {
+    angle_delta: i8, // -1, 0, +1
+    power_delta: i8, // -1, 0, +1
+    fire: bool,
+
+    pub const NONE: Input = .{
+        .angle_delta = 0,
+        .power_delta = 0,
+        .fire = false,
+    };
+};
+
+pub fn initGame(terrain: *const Terrain) GameState {
+    const p1_x = Fixed.fromInt(100);
+    const p2_x = Fixed.fromInt(700);
+
+    return .{
+        .tick = 0,
+        .current_turn = 0,
+        .wind = Fixed.ZERO,
+        .players = .{
+            .{
+                .x = p1_x,
+                .y = terrain.heightAt(p1_x),
+                .cannon_angle = Fixed.fromFloat(0.785), // ~45 degrees
+                .power = Fixed.fromInt(50),
+                .health = 100,
+                .alive = true,
+            },
+            .{
+                .x = p2_x,
+                .y = terrain.heightAt(p2_x),
+                .cannon_angle = Fixed.fromFloat(2.356), // ~135 degrees
+                .power = Fixed.fromInt(50),
+                .health = 100,
+                .alive = true,
+            },
+        },
+        .projectile = null,
+        .terrain = terrain,
+        .rng_state = 0,
+    };
+}
+
+pub fn simulate(state: *GameState, inputs: [2]Input) void {
+    const current = state.current_turn;
+    const input = inputs[current];
+    var player = &state.players[current];
+
+    // apply input only when no projectile in flight
+    if (state.projectile == null) {
+        // adjust angle
+        const angle_adj = ANGLE_SPEED.mul(Fixed.fromInt(input.angle_delta));
+        player.cannon_angle = player.cannon_angle.add(angle_adj).clamp(MIN_ANGLE, MAX_ANGLE);
+
+        // adjust power
+        const power_adj = POWER_SPEED.mul(Fixed.fromInt(input.power_delta));
+        player.power = player.power.add(power_adj).clamp(MIN_POWER, MAX_POWER);
+
+        // fire
+        if (input.fire) {
+            const cos_a = trig.cos(player.cannon_angle);
+            const sin_a = trig.sin(player.cannon_angle);
+            const speed = player.power.mul(PROJECTILE_SPEED_FACTOR);
+
+            // flip vx for player 1 (facing right uses positive cos)
+            // player 0 at x=100 faces right, player 1 at x=700 faces left
+            const vx = if (current == 0) speed.mul(cos_a) else speed.mul(cos_a).neg();
+
+            state.projectile = .{
+                .x = player.x,
+                .y = player.y.add(Fixed.fromInt(20)), // spawn above player
+                .vx = vx,
+                .vy = speed.mul(sin_a),
+            };
+        }
+    }
+
+    // update projectile physics
+    if (state.projectile) |*proj| {
+        // gravity (downward)
+        proj.vy = proj.vy.sub(Fixed.GRAVITY);
+
+        // wind
+        proj.vx = proj.vx.add(state.wind.mul(Fixed.WIND_FACTOR));
+
+        // movement
+        proj.x = proj.x.add(proj.vx);
+        proj.y = proj.y.add(proj.vy);
+
+        var hit = false;
+
+        // terrain collision
+        const terrain_y = state.terrain.heightAt(proj.x);
+        if (proj.y.lessThan(terrain_y)) {
+            hit = true;
+        }
+
+        // player collision
+        for (&state.players) |*p| {
+            if (p.alive and hitTest(proj, p)) {
+                p.health -= DAMAGE;
+                if (p.health <= 0) p.alive = false;
+                hit = true;
+            }
+        }
+
+        // out of bounds (left/right)
+        if (proj.x.lessThan(Fixed.ZERO) or proj.x.greaterThan(Fixed.fromInt(@intCast(SCREEN_WIDTH)))) {
+            hit = true;
+        }
+
+        // out of bounds (too high - prevent infinite flight)
+        if (proj.y.greaterThan(Fixed.fromInt(2000))) {
+            hit = true;
+        }
+
+        if (hit) {
+            state.projectile = null;
+            state.current_turn = 1 - current;
+        }
+    }
+
+    state.tick += 1;
+}
+
+fn hitTest(proj: *const Projectile, player: *const Player) bool {
+    const dx = proj.x.sub(player.x).abs();
+    const dy = proj.y.sub(player.y).abs();
+    return dx.lessThan(HIT_RADIUS) and dy.lessThan(HIT_RADIUS);
+}
+
+// tests
+
+test "initGame creates valid state" {
+    const terrain = @import("terrain.zig").generateFixed();
+    const state = initGame(&terrain);
+
+    try std.testing.expectEqual(@as(u32, 0), state.tick);
+    try std.testing.expectEqual(@as(u8, 0), state.current_turn);
+    try std.testing.expect(state.projectile == null);
+    try std.testing.expect(state.players[0].alive);
+    try std.testing.expect(state.players[1].alive);
+}
+
+test "simulate advances tick" {
+    const terrain = @import("terrain.zig").generateFixed();
+    var state = initGame(&terrain);
+
+    simulate(&state, .{ Input.NONE, Input.NONE });
+    try std.testing.expectEqual(@as(u32, 1), state.tick);
+
+    simulate(&state, .{ Input.NONE, Input.NONE });
+    try std.testing.expectEqual(@as(u32, 2), state.tick);
+}
+
+test "fire creates projectile" {
+    const terrain = @import("terrain.zig").generateFixed();
+    var state = initGame(&terrain);
+
+    const fire_input: Input = .{ .angle_delta = 0, .power_delta = 0, .fire = true };
+    simulate(&state, .{ fire_input, Input.NONE });
+
+    try std.testing.expect(state.projectile != null);
+}
+
+test "projectile moves" {
+    const terrain = @import("terrain.zig").generateFixed();
+    var state = initGame(&terrain);
+
+    // fire
+    const fire_input: Input = .{ .angle_delta = 0, .power_delta = 0, .fire = true };
+    simulate(&state, .{ fire_input, Input.NONE });
+
+    const initial_x = state.projectile.?.x;
+    const initial_y = state.projectile.?.y;
+
+    // advance
+    simulate(&state, .{ Input.NONE, Input.NONE });
+
+    // projectile should have moved
+    try std.testing.expect(!state.projectile.?.x.eq(initial_x) or !state.projectile.?.y.eq(initial_y));
+}
+
+test "angle adjustment" {
+    const terrain = @import("terrain.zig").generateFixed();
+    var state = initGame(&terrain);
+
+    const initial_angle = state.players[0].cannon_angle;
+
+    const up_input: Input = .{ .angle_delta = 1, .power_delta = 0, .fire = false };
+    simulate(&state, .{ up_input, Input.NONE });
+
+    try std.testing.expect(state.players[0].cannon_angle.greaterThan(initial_angle));
+}
diff --git a/src/main.zig b/src/main.zig
index c646904..c05119d 100644
--- a/src/main.zig
+++ b/src/main.zig
@@ -3,41 +3,113 @@ const rl = @import("raylib");
 
 const Fixed = @import("fixed.zig").Fixed;
 const trig = @import("trig.zig");
+const terrain_mod = @import("terrain.zig");
+const game = @import("game.zig");
 
-const SCREEN_WIDTH = 800;
-const SCREEN_HEIGHT = 600;
+const Terrain = terrain_mod.Terrain;
+const GameState = game.GameState;
+const Input = game.Input;
+
+const SCREEN_WIDTH = terrain_mod.SCREEN_WIDTH;
+const SCREEN_HEIGHT = terrain_mod.SCREEN_HEIGHT;
 
 // colors (vector/oscilloscope aesthetic)
 const BG_COLOR = rl.Color{ .r = 10, .g = 10, .b = 18, .a = 255 };
 const CYAN = rl.Color{ .r = 0, .g = 255, .b = 255, .a = 255 };
 const MAGENTA = rl.Color{ .r = 255, .g = 0, .b = 255, .a = 255 };
 const GREEN = rl.Color{ .r = 0, .g = 255, .b = 0, .a = 255 };
+const YELLOW = rl.Color{ .r = 255, .g = 255, .b = 0, .a = 255 };
 
 pub fn main() !void {
-    rl.initWindow(SCREEN_WIDTH, SCREEN_HEIGHT, "lockstep");
+    rl.initWindow(@intCast(SCREEN_WIDTH), @intCast(SCREEN_HEIGHT), "lockstep artillery");
     defer rl.closeWindow();
     rl.setTargetFPS(60);
 
-    // test fixed-point math
-    const angle = Fixed.ZERO;
-    const sin_val = trig.sin(angle);
-    const cos_val = trig.cos(angle);
+    // initialize game
+    const terrain = terrain_mod.generateFixed();
+    var state = game.initGame(&terrain);
 
     while (!rl.windowShouldClose()) {
+        // gather input for current player
+        const input = gatherInput();
+
+        // simulate (both players' inputs, but only current player acts)
+        var inputs: [2]Input = .{ Input.NONE, Input.NONE };
+        inputs[state.current_turn] = input;
+        game.simulate(&state, inputs);
+
+        // render
         rl.beginDrawing();
         defer rl.endDrawing();
 
         rl.clearBackground(BG_COLOR);
 
-        // draw some test lines
-        rl.drawLine(100, 500, 700, 500, GREEN);
-        rl.drawLine(200, 300, 200, 500, CYAN);
-        rl.drawLine(600, 300, 600, 500, MAGENTA);
-
-        // show fixed-point values
-        var buf: [128]u8 = undefined;
-        const text = std.fmt.bufPrintZ(&buf, "sin(0)={d:.3} cos(0)={d:.3}", .{ sin_val.toFloat(), cos_val.toFloat() }) catch "?";
-        rl.drawText(text, 10, 10, 20, rl.Color.white);
-        rl.drawText("lockstep artillery - phase 1 complete", 10, 40, 20, GREEN);
+        drawDebugInfo(&state);
     }
 }
+
+fn gatherInput() Input {
+    var input = Input.NONE;
+
+    // angle: up/down arrows
+    if (rl.isKeyDown(.up)) input.angle_delta = 1;
+    if (rl.isKeyDown(.down)) input.angle_delta = -1;
+
+    // power: left/right arrows
+    if (rl.isKeyDown(.right)) input.power_delta = 1;
+    if (rl.isKeyDown(.left)) input.power_delta = -1;
+
+    // fire: space
+    if (rl.isKeyPressed(.space)) input.fire = true;
+
+    return input;
+}
+
+fn drawDebugInfo(state: *const GameState) void {
+    var buf: [256]u8 = undefined;
+    var y: i32 = 10;
+    const line_height: i32 = 20;
+
+    // tick and turn
+    const turn_text = std.fmt.bufPrintZ(&buf, "tick: {d}  turn: player {d}", .{ state.tick, state.current_turn }) catch "?";
+    rl.drawText(turn_text, 10, y, 16, rl.Color.white);
+    y += line_height;
+
+    // player 0 info
+    const p0 = &state.players[0];
+    const p0_text = std.fmt.bufPrintZ(&buf, "P0: angle={d:.2} power={d:.0} health={d}", .{
+        p0.cannon_angle.toFloat(),
+        p0.power.toFloat(),
+        p0.health,
+    }) catch "?";
+    rl.drawText(p0_text, 10, y, 16, CYAN);
+    y += line_height;
+
+    // player 1 info
+    const p1 = &state.players[1];
+    const p1_text = std.fmt.bufPrintZ(&buf, "P1: angle={d:.2} power={d:.0} health={d}", .{
+        p1.cannon_angle.toFloat(),
+        p1.power.toFloat(),
+        p1.health,
+    }) catch "?";
+    rl.drawText(p1_text, 10, y, 16, MAGENTA);
+    y += line_height;
+
+    // projectile info
+    if (state.projectile) |proj| {
+        const proj_text = std.fmt.bufPrintZ(&buf, "projectile: x={d:.1} y={d:.1} vx={d:.2} vy={d:.2}", .{
+            proj.x.toFloat(),
+            proj.y.toFloat(),
+            proj.vx.toFloat(),
+            proj.vy.toFloat(),
+        }) catch "?";
+        rl.drawText(proj_text, 10, y, 16, YELLOW);
+    } else {
+        rl.drawText("projectile: none (press SPACE to fire)", 10, y, 16, YELLOW);
+    }
+    y += line_height;
+
+    // controls
+    y += line_height;
+    rl.drawText("controls: UP/DOWN=angle  LEFT/RIGHT=power  SPACE=fire", 10, y, 14, rl.Color.gray);
+}
diff --git a/src/terrain.zig b/src/terrain.zig
new file mode 100644
index 0000000..880543c
--- /dev/null
+++ b/src/terrain.zig
@@ -0,0 +1,73 @@
+// terrain generation and collision
+// deterministic - no floats, no randomness (for now)
+
+const Fixed = @import("fixed.zig").Fixed;
+
+pub const SCREEN_WIDTH: usize = 800;
+pub const SCREEN_HEIGHT: usize = 600;
+
+pub const Terrain = struct {
+    heights: [SCREEN_WIDTH]Fixed,
+
+    pub fn heightAt(self: *const Terrain, x: Fixed) Fixed {
+        const ix = x.toInt();
+        if (ix < 0) return Fixed.ZERO;
+        if (ix >= SCREEN_WIDTH) return Fixed.ZERO;
+        return self.heights[@intCast(ix)];
+    }
+};
+
+// fixed pattern: parabolic hills for testing
+// produces gentle rolling terrain
+pub fn generateFixed() Terrain {
+    var t: Terrain = undefined;
+    for (0..SCREEN_WIDTH) |i| {
+        // base height + parabolic hills
+        // creates two bumps across the screen
+        const base: i32 = 100;
+        const x: i32 = @intCast(i);
+
+        // two hills centered at x=200 and x=600
+        const hill1 = hillHeight(x, 200, 80, 150);
+        const hill2 = hillHeight(x, 600, 80, 150);
+
+        const height = base + hill1 + hill2;
+        t.heights[i] = Fixed.fromInt(height);
+    }
+    return t;
+}
+
+// parabolic hill: peak at center, width determines spread
+fn hillHeight(x: i32, center: i32, peak: i32, width: i32) i32 {
+    const dist = x - center;
+    if (dist < -width or dist > width) return 0;
+    // parabola: peak * (1 - (dist/width)^2)
+    const ratio_sq = @divTrunc(dist * dist * 100, width * width);
+    return @max(0, peak - @divTrunc(peak * ratio_sq, 100));
+}
+
+const std = @import("std");
+
+test "terrain heightAt bounds" {
+    const t = generateFixed();
+
+    // valid positions return height
+    const h = t.heightAt(Fixed.fromInt(400));
+    try std.testing.expect(h.raw > 0);
+
+    // out of bounds returns zero
+    try std.testing.expect(t.heightAt(Fixed.fromInt(-10)).eq(Fixed.ZERO));
+    try std.testing.expect(t.heightAt(Fixed.fromInt(900)).eq(Fixed.ZERO));
+}
+
+test "terrain has hills" {
+    const t = generateFixed();
+
+    // hill peaks should be higher than edges
+    const edge = t.heightAt(Fixed.fromInt(0)).toInt();
+    const peak1 = t.heightAt(Fixed.fromInt(200)).toInt();
+    const peak2 = t.heightAt(Fixed.fromInt(600)).toInt();
+
+    try std.testing.expect(peak1 > edge);
+    try std.testing.expect(peak2 > edge);
+}