Da Vinci Code objects
From Halopedia, the Halo wiki
The Da Vinci Code objects are objects that appear in several levels in Halo 3, and Halo 3: ODST. These objects are textured with a default UV-unwrapped texture (used to render textures onto 3D models). The texture is called a default texture, because the final rendered texture was never wrapped, for reasons unknown. The image consists of a spectrum colored grid, with each tile containing a letter from A to P in lowercase and alphabetical order. Each line repeats the one above, albeit shifted right by one letter. The name was likely inspired from the texture's slight visual similarity to the "cryptex" featured in Dan Brown's The Da Vinci Code.
Given that these objects are found near or in interactive, functioning parts of the map, (Inside Sandbox's laser towers, in Heretic's gravity lifts, etc.) it can be assumed that their purpose is one of a technical nature.
On Sandtrap and Sandbox, spherical objects dubbed "Easter eggs" and also known as "Da Vinci Eggs", are located near or inside large, tower-like Forerunner structures, and in both levels serve to keep the player from exiting the level. Despite being called Easter eggs, these items were never intended to be discovered by players, they are mere anomalies left in the final version of the game for unknown reasons.
In Sandtrap, the eggs fire orange beams into the sand whenever a player tries to exit the map; these beams activate brute landmines that are buried along the level's perimeter. A landmine will trigger wherever the beam hits the ground. The beams themselves are harmless, unlike the beams on Sandbox. In both cases, the eggs' kills are attributed to The Guardians.
In Sandbox, the eggs fire much more powerful beams directly at escaping players, killing such players almost instantly. The beams on Sandbox are much more accurate, as they were meant to target specific players. However, unlike the beams on Sandtrap, Sandbox's beams can be blocked by bubble shields and most Forge objects. These beams are very similar to the projectiles fired by a Gauss Warthog.
To see the eggs, two players must cooperate. One player (Person A) must, while in Edit Mode, exit the map from the Sky Bubble by spawning a teleporter outside the map. Person A must then fly to a tower (but watch out for kill barriers) and spawn a turret against the light in the tower. A second player (Person B) must then man the turret and have Person A pick the turret up. Person A should drag Person B up the wall while B is still against it. Towards the middle of the light, the Easter egg can be seen.
Da Vinci Cube
On Heretic, an untextured cube is hidden inside each of the lifts at the center of the map. To reach one of these "Da Vinci Cubes", a player must place a Machine Gun Turret against the top of the lift. They should then proceed to use the Forge turret glitch to enter the small compartment that holds the cube.
The Da Vinci Cubes power their respective lifts; overloading the map will cause the cubes to vanish, disabling the accompanying lifts. There are only four known Da Vinci Cubes on Heretic. The lifts on Sandtrap are powered by something like cubes; there is a little 2D green square under both lifts, and the ones on Valhalla are man cannons, and man cannons don't have cubes. Interestingly, the Cubes are noticeably smaller than the Easter Eggs on Sandtrap and Sandbox.
Da Vinci Towers
In the Halo 3 campaign level The Covenant, the Time travel glitch can be used to reveal two Da Vinci Towers hidden outside the level boundaries. The towers do not appear in normal gameplay, but seem to be glitched or altered copies of the shield-generating towers that the level's objectives center around. Most of the towers' surfaces are untextured, and the non-solid towers don't appear to serve any purpose.
It is possible that Bungie created two versions or layers of the normal shield-generating towers. The outer layer is immutable, but the inner layer (the "Da Vinci" layer) will vanish if the shield generators in the towers are disabled. It is entirely possible that the Da Vinci Towers are projecting the beams that power the shields, which would explain why disabling the shields removes the towers.
Da Vinci Sphere
In the Campaign level Halo, during the battle against 343 Guilty Spark, a small "Da Vinci" spherical object can be seen inside him. The sphere can only be seen when he is heavily damaged, and will disappear when he explodes.
The sphere seems to power Spark's laser, as it can't be seen in a forge monitor. It also appears to be more rounded than the "Da Vinci" spheres on Sandtrap and Sandbox. There is also another much smaller sphere inside Spark, but it is unknown if this sphere has "Da Vinci" textures.
Halo 3: ODST objects
Other "Da Vinci" code objects have been found in Halo 3: ODST.
In the campaign level Kizingo Boulevard, there is a very large flat "Da Vinci" rectangle outside the map southwest of Mombasa Island, on the level floor. The shape has no strategic placement and is surrounded by a void. A void contains no textures nor solids, and is empty, hence called a void. It is possible for the player to reach the object without theater mode, using the Banshee hijack glitch.
ONI Alpha Site
In ONI Alpha Site, there are more rectangular "Da Vinci" objects near the bottom of the elevator shafts in the lobby. The shapes can be seen by jumping over the walls (where the elevator comes up) and fall to the bottom. The text on the rectangles appear to be upside-down and very thin. The rectangles can also be seen on Alpha Site.
Note: If the player shoots the walls around the objects, they will splash as if you were shooting water.