Tale of Diep:Perpendiculus

''While somewhat smaller than the rest of his brethren, the one with four sides is still a force to be reckoned with. He specializes in overwhelming his opponents in number, swarming them with countless enemies until they retreat or are destroyed by his hand. It's best to avoid this one if you're not adequately prepared to face nigh-endless waves of enemies and that ridiculously large ego of his.''

Overview
Perpendiculus is one of the eight Disciples of the Polygons. Being the second to be created, his mindset is to immediately populate every province of the realm of his beloved four-sided shapes. However, recent times now in the are tough. It is unfortunate how the square's structure is easy to be manipulated and transformed into mindless soldiers, and those who are Necromancers are highly appalling. Perpendiculus has a burning grudge against due to this, almost making him eager to burst out of his fortress confine and face the Lich head on, even if the, and the other Disciples warn him not to (he tried many times before...). Perpendiculus doesn't like tanks that utilize square-shaped bodies, he calls them square-wannabes and will most certainly target them first. Being the second "oldest" doesn't necessarily mean he's the most mature...

Perpendiculus represents the Squares and every defender associated with them. Despite being the leader of the currently weakest polygons, he is far from being easy. Perpendiculus, along with the other Polygon Disciples, is located within the heart of a Polygon Fortress. He is located in the midst of a formidable desert known as Paradigm Dunes. In the game mode where the Polygon Mother herself is fought within a massive structure, each Disciple, including Perpendiculus, has an independent space in which where they are battled. He lies within the Square Fortress, a structure filled with the Square-based inhabitants and the keepers that await any intruders. They will be fought first before facing down the ruler of them all.

Music


Design
Perpendiculus has a large yellow square body and four arms, made up of four smaller squares connecting four larger squares (about half the size of the body and represent hands) to the body itself. Two of the arms are Summoner Square orange-colored. Perpendiculus also wears a thin helmet with a square gem embedded in it. He has a spawner on his base, and two arms have spawners while the other two have Sentry Square-like barrels.

Stats
Perpendiculus has a total HP of 39,400. He has a 25% resistance to damage. Perpendiculus regenerates very slowly, 3 HP every second for all parts, regeneration does increase by 500% if left alone for over two minutes (though it's rare for that to happen). He has a base body damage of 50 HP.

Perpendiculus can summon various square-based polygon types, to even bosses such as the Summoner and the, or even the. He has an ability to summon many as well. The hands with the spawners will only create crasher-based enemies. In Phase 2, where his hands lose their weapons, Perpendiculus can summon boss entities.

Perpendiculus's bottom spawner spawns normal squares at 40% the rate of a Summoner. There is a 25% chance for a square to be a Summoner Square and a 5% chance for it to be a Splitter Square. Swarm Squares come from Splitter Squares, so there is no need for them to spawn on their own. Occasionally, instead of a square, a clump of 3-5 Splitter Squares is released instead with an audible "thunk", and Perpendiculus's spawner can be seen shaking slightly after spawning the clump of Splitter Squares. 10-12 Summoner Squares are occasionally released instead of a normal Summoner Square. There is a maximum of 800 square-related things spawned by his spawner in both phases, NOT to squares or square-related things spawned during attacks, which have a limit of 1400 square-related things total (one individual Swarm Square is counted as 1/4th of a square for both limits). That's a lot, and summing both limits allows Perpendiculus to have up to 2200 squares total. Perpendiculus's hand spawners usually spawn only Summoner Squares at 75% of the rate of a Summoner, however, they also can spawn the occasional Splitter Square. The gun hands just fire as normal. His hand spawners stop spawning squares if used in an attack or otherwise noted.

Perpendiculus's attacks involve both some bullet firing and directing around Crashers and squares in special formations, however, most attacks involve some form of swarming with squares.

Phase 1
During this phase of the battle, he is in the center of the arena, staying still as more players join in. He is invulnerable during this as a transmission from the Polygon Mother warns the tanks once more about the dangers they are about to face down, and that Perpendiculus should be left alone. After the transmission ends, Perependiculus stands up and speaks his one quote right after he makes his first and only attack, which causes about 20 Beta Squares to block up the exit. Polygons created by Perpendiculus will not reward any EXP.

Perpendiculus is invulnerable during Phase 1, and only when his hands' HP reaches 0 will cause him to enter Phase 2. The hands that are "destroyed" lose all of their weapons and become invulnerable but useless. Attacks that require the weapons will be disabled.


 * SWARM!: 20 Beta Squares with a circle on one side with a lance and helmets come up to block the exit. They block anyone from coming in or going out, pushing them back while dealing no damage. They are also Invincible. This attack will only occur once.

It's swarm time, puny tanks!
 * Square Swarm: Perpendiculus spawns 75-110 Summoner Squares or 160-220 Swarm Squares in front of him. He then directs it in one group, in a fat line formation. Existing squares are not affected.
 * Fist Armor: Perependiculus gains 8 Yellow Squares and Summoner Squares (alternating 4 and 4) circling each of his hands, 32 in total. He then starts punching tanks and dealing medium damage with each punch, stacked on top of the additional Squares' body damage. Each square that is a part of the fist armor will have 100 HP and will deal 12 HP of body damage. Summoner Squares that are destroyed will break off and chase the players.
 * Pew Pew: Perependiculus fires off 5 shots from each of his gun hands in random trajectories. Bullets do medium damage and are pretty fast. Repeated 3-5 times in quick succession.
 * Spawner Wake: Perpendiculus rotates his spawner hands back and forth as he launches out high-speed Summoner Squares, which travel in one direction only and die when they hit something. Each spawner releases about 10-12 squares total. Repeated 2-3 times, but with a pause in between.
 * Squarenova: Perpendiculus stops spawning squares, and gathers every single square type in the room together into a clump. He then expands it out at high speed, with lots of squares flying everywhere to deal low damage that stacks up with more things that hit you.
 * Square Wannabes: Used only if there is a Necromancer, Factory, or Hellfire currently in the room. If it is a Hellfire, Perpendiculus fires a Streamliner formation from both of his barrels onto it. If it is a Necromancer, he directs all existing Summoner Squares onto it. If it is a Factory, he charges and punches it four times with his spawner hands while still spawning squares.
 * Four Times The Fun: Gathers all existing squares into a giant invincible square with different colors. If there are leftovers, he lets them be. Perpendiculus jumps on top of the giant square and spawns 4 Alpha Squares next to him, flinging them all at once at tanks. The square throwing part is then repeated 2 more times. The giant square then disintegrates into individual squares again.
 * Square-a-pult: Perpendiculus spawns 12 Beta Squares forming a 4x4 square around him, with the middle 4 squares missing. He then grabs 3 in each hand and aims them at tanks, flinging them out at 22.5-degree trajectories centered on the middle squares.
 * Lateral Strike: Perpendiculus summons 4 holographic Beta Squares (same color as usual) and flings them at players at right angles to the direction in which he is currently facing.
 * Square-off: Perpendiculus summons 4 square and sends them to attack tanks. There can be duplicates. Usually used at least 45 seconds after the last of the previous 5 have been destroyed.
 * Rightened Lightning: Perpendiculus fires 4 lightning streams from each hand, doing high damage and inflicting for 10 seconds. The lightning moves rather slowly in a sine-wave pattern, only obstructed by the fortress walls.
 * Square Bolt: Perpendiculus fires 16 short yellow lightning bolts that move incredibly fast, dealing low damage on contact (damage ticks once) and inflicting Paralyzed for 4 seconds. These bolts bounce off things at random angles 5 times before disappearing. Only happens 3 times during Phase 1, it happens every 14 attacks.
 * Quadrilateral Bombardment: Perpendiculus will release a laugh as both of his square cannons point upward, firing a bunch of squares quickly upward off-screen. Yellow square shaped targets will begin to dot the map, slowly becoming red. There will be tens of these quickly appearing over the course of about six seconds. When a target becomes fully red, it will flash, vanish, and a Yellow Square will land there, firing four bullets evenly spaced outward. Players standing in the target when the Square hits will take minor damage + the Square's body damage. The bullets themselves do much more damage. Perpendiculus' cannon arms are Armored as this ability happens.
 * Square Man: Perpendiculus encases himself in a giant square, and moves around Invincible, smashing into players to deal his normal body damage.
 * Quasar Squared: Only happens when Decratite is alive unless battling. A blue portal forms in front of Perpendiculus, catching him off guard while a quote from Decratite is said. He is invulnerable while the quote is being said. 8 Yellow Quasar types fly out of the portal and invade the arena. Perpendiculus will resume his attacks immediately after. Only happens 2 times during Phase 1, it happens every 16 attacks.

Phase 2
When Perependiculus's hands are disabled, he enters Phase 2. Perpendiculus moves faster and now starts summoning lots of minions. He teleports into the center of the arena at the very beginning of Phase 2. Bullets fired at the hands will go through them. Perpendiculus's square gem on his helmet glows brighter and the helmet cracks slightly.

Perpendiculus can now summon bosses such as the Summoner,, and. All of these bosses will reward EXP, excluding their minions.

During a boss summon, Perpendiculus will be invulnerable until the boss/bosses dies. He cannot attack while a boss is in session. After the boss dies, Perpendiculus will resume attacking until the loss of 3,000 HP has been reached. For every 3,000 HP lost, Perpendiculus will summon a boss or multiple bosses as the following:

Boss Spawning Order:

 * At 21,400 HP: The Summoner.
 * At 18,400 HP: The Constructionist.
 * At 15,400 HP: Two Summoners or Constellation or Spartan.
 * At 12,400 HP: Two Constructionists or Constellation + Summoner or Spartan + Constructionist.
 * At 9,400 HP: Constellation + Constructionist or Four Summoners or Two Constructionists + Summoner or Two Spartans.
 * At 6,400 HP: Two Constellations or Five Summoners or Four Constructionists or Three Spartans.
 * At 3,400 HP: Two Constellations + Summoner or Six Summoners or Four Constructionists or Two Summoners + Spartan + Constructionist
 * At 400 HP: Two Constellations + Four Summoners + Four Constructionists + Three Spartans.

Attacks
During the between sessions of the boss summoning, Perpendiculus will do these attacks randomly. If Perpendiculus reaches a 3,000 HP mark, he'll become invulnerable and waits for the attack to be finished.


 * Square Swarm II: Perpendiculus spawns 120-175 Summoner Squares or 250-300 Swarm Squares in front of him. He then directs it in one group, in a fat line formation. Existing squares are not affected.
 * Squarenova II: Perpendiculus stops spawning squares, and gathers every single square type in the room together into a clump. He then expands it out at high speed, with lots of squares flying everywhere to deal low damage that stacks up with more things that hit you. However, Perpendiculus repeats this until there are no squares left or 5 explosions have occurred.
 * Four Times The Fun II: Gathers all existing squares into a giant invincible square with different colors. If there are leftovers, he lets them be. Perpendiculus jumps on top of the giant square and spawns 8 Alpha Squares next to him, flinging them all at once at tanks. The square throwing part is then repeated 2 more times. The giant square then disintegrates into individual squares again.
 * Square-a-pult II: Perpendiculus spawns 12 Beta Squares forming a 4x4 square around him, with the middle 4 squares missing. Since he lacks the heavy use of his hands, he uses existing Summoner Squares and Swarm Squares to manipulate the Beta Squares now. He throws them faster, more accurately, and as a result of the impact, the thrown squares do slightly more damage.
 * Square-off II: Perpendiculus summons 8 square and sends them to attack tanks. There can be duplicates. Usually used at least 45 seconds after the last of the previous 5 have been destroyed.
 * Rightened Lightning II: Perpendiculus fires 4 lightning streams from each hand, doing high damage and inflicting for 15 seconds. The lightning moves significantly faster in the same sine-wave pattern, this time bouncing off of the fortress walls once.
 * Square Man II: Perpendiculus encases himself in a giant square, and moves around Invincible, smashing into players to deal body damage. He will also do knockback and send players bouncing off the walls now.
 * Quadrilateral Squared: Perpendiculus puts down a normal yellow square that glows white, which then starts multiplying from 1 square to 2, 4, 16, and finally 256 squares just to make a mess in the room. Doesn't do anything much, just creates a huge obstacle that needs to be destroyed.
 * Square Root: Perpendiculus stops in place, stops spawning squares, becomes, and spawns 10 Nest Defenders to fight. He heals 2500 health in the meantime. Cannot be used more than 3 times in this phase.
 * Square In The Head: Perpendiculus summons five Beta Squares, and tosses them right on top of tanks. Said tanks are immobile until their allies destroy the squares on top of them. They can still fire, but not hit the square directly unless they have drones or a top-mounted Auto Turret.
 * Square You: Perpendiculus picks up a tank, and flattens it into a square, dealing low damage. This is only aesthetic, other than the low damage. The flattened tank will pop back into shape 45-75 seconds later, regardless of its original body shape.
 * Squares Squares Squares!: Perpendiculus summons 225 squares that orbit around him, blocking attacks. He clumps them up in various formations to block ammunition, but this leaves other openings where players can fire stray bullets through. However, he will attempt to block as much ammunition as he can until most of the squares are destroyed, at which point he will just have them in a ring around him.
 * Square Slash: Perpendiculus's resourcefulness comes in handy here. He forms any nearby squares into a sword, which he then controls to slash at players to deal medium-low to very high damage, depending on what type of squares players are hit by.
 * Ssssssquare: Perpendiculus summons 5-10 Square Snakes, which is a featureless entity made of 10 squares linked in a line and slithers around. These things are pretty much harmless and can't attack any way other than body damage (they serve mostly to get in the way), and since they are made of 10 normal squares, most players will make very short work of them.

The End of Perpendiculus
When Perpendiculus reaches the 400 HP mark and after the bosses are defeated, a transmission from the Polygon Mother reminds the tanks about what they are about to face with. Perpendiculus will then use a deluxe version of Square Swarm II, summoning a mass of about 500 Swarm Squares. The guards at the door also become active, and Perpendiculus allows his Swarm Squares to go every which way, causing loads of chaos. He will continually summon any more Swarm Squares (not from his spawner, somewhere randomly in the battle room), one for each one lost. He will also be actively moving around to avoid ammunition.

Each Beta Square guard has 600 HP. They deal 9 HP of body damage per hit. They attack through swiping the little lances they hold and attack quite fast. They are pretty fast, too. The lance does a considerable amount of damage to tanks. The guards aren't necessary to defeat the boss, just deal enough damage to Perpendiculus and this is all over...

If every tank present during Perpendiculus's final moment has died, a transmission from the Polygon Mother to those engaged in Perpendiculus's battle will appear, her congratulating them for "sparing" Perpendiculus. The entrance to his fortress will be blocked for 45 minutes, and everything will get reset.

However, if Perpendiculus's HP finally reaches 0, he kneels down and white cracks begin forming all around his body, with any square in range around him starting to lose their color, turning into shades of gray. Perpendiculus then suddenly vaporizes with a white flash on the screen, leaving only the helmet behind on top of a pile of ashes. All squares and polygons associated to them with a huge radius around the death of Perpendiculus will have halved HP and resistances. Any square-based bosses/ that were present near the fortress where Perpendiculus has been defeated will greatly reduce in HP and Resistances, Inferior Square nests will stop spawning squares for a long time around its destruction area...

Rewards
* To be added*

Introduction During Battle
(Awaiting additional ones)
 * "I have four sides. As for you all, you all have none. I have four arms. You all have none among you. Four is far greater and more significant than none. Therefore, I can and will vanquish you pathetic round beings! Ah ha ha HAW!"
 * "... They avenged me! My fellow squares have... AVENGED ME! ... HAW! Let's get this straight, so you failed to keep your puny selves from being bombarded from my fantastic squares!? HAWWWW!!! ... Let this be known, FOUR SIDES are FAR GREATER THAN NONE. I'll make you cry! --- SWARM THEM!" (If Perpendiculus has been defeated twice in a row and rematched again if he respawns in The Realm prior to the Ascension)
 * "Alright, ALRIGHT! This is getting irritating... You choose ME to get rid of first, and I keep coming back because your forces are unable to keep myself away? This is so STUPID! Just give up and say that I'm RIGHT, LEAVE US ALONE!!! Ha... ha... hawwww... * Long pause*... You know I'm the best, or at least better than your stupid forces... * With hesitation*... SWARM THEM!!!" (If Perpendiculus has been defeated a third time consecutively and rematched again if he respawns in The Realm prior to the Ascension)
 * "... So we meet again... AGAIN! This is starting to get boring I say! Your terrible army has failed, again! ... Hey, let's not fight so much now? I HAVE BETTER THINGS TO DO!!! * Quietly* Swarm them..." (Said randomly if Perpendiculus has been defeated more than three times and rematched again if he respawns in The Realm prior to the Ascension)

Phase 1

 * "Ah ha ha haw, tanks! You're circular, and therefore POINTLESS!" (Said randomly)
 * "Ready the swarm!" (Said randomly)
 * "I'm gonna take the square root of you!" (Said randomly)
 * "My angles compliment each other nicely!" (Said randomly)
 * "I could kill you with my smile!" (Said randomly, revealing an even creepier bracket smile)
 * "Be there or be square they said! And you didn't choose RIGHT!" (Said randomly)
 * "HAW HAW HAW HAW! Square up!" (Sometimes said before using Fist Armor)
 * "I have four times the fun! You all have none! Ah haw haw haw haw!" (Sometimes said before using Four Times the Fun)
 * "Imposter! What kind of mockery is this you stupid square wannabes!?" (Said before Square Wannabe)
 * "Swarm them! While they can't move! HAWWWW!" (Sometimes said before Rightened Lightning)
 * "Ah ha ha ha HAWWWW!" (Said before Quadrilateral Bombardment)
 * "You cannot hurt me now, stupid circles!" (Sometimes said before Square Man)
 * "HAWWW? What are you saying, my beloved squares? It's too crowded in here? That was fast!"(Said if either square limit is reached within 180 seconds of Phase 1)
 * "Is it getting cramped in here, little pointless ones? Regardless, I'd be happy to end your claustrophobia by KILLING YOU! HAW HAW HAW! SWARM THEM!" (Said if Perpendiculus reaches both square limits at the same time in either Phase 1 or Phase 2, only said once in both phases. Perpendiculus will also smile even wider.)

Phase 2

 * "HAWWW? You crushed my weapons! How can this be, ruining my fancy gadgets... pitiful! Alas, I don't need them! ITS SWARM TIME, PUNY TANKS!" (Said when changing into Phase 2)
 * "I don't need weapons to destroy you! I have swarms!" (Said randomly)
 * "It's my job to protect the squares. And you're REALLY getting in the way of that!" (Said randomly)
 * "I knew stupid no-siders like you wouldn't understand the problems of the polygons!" (Said randomly)
 * "Killing me will only bring The Realm harm!" (Said randomly)
 * "Have your kind ever felt like what it been to be FARMED!?" (Said randomly)
 * "We still surround and outnumber you four thousandfold! One for every tank and four for every side! Ah haw haw haw!" (Said randomly)
 * "You know what they say about squares! That they're always RIGHT!" (Said randomly)
 * "Take your value and divide it by your sides! That's what you're really worth!" (Said randomly)
 * "Swarming you is what I'm all about!" (Said randomly)
 * "We need more squares, lemme call in the elite!" (One of many quotes that can be said before a boss summoning)
 * "You know squares as weak, but we can prove you wrong!" (One of many quotes that can be said before a boss summoning)
 * "THE SWARM NEVER ENDS! AH HAW HAW HAW HAWWWWWWWWW!" (One of many quotes that can be said before a boss summoning)
 * "Protect me in my finest hour!" (Sometimes said before using Squares Squares Squares!)
 * "Now I'm REALLY gonna take the square root of you!" (Sometimes said before using Square You)

Quotes that Perpendiculus said in Phase 1 for attacks that also have a second variant in Phase 2 will retain their quotes here as well.

Death Phase

 * " * heavy breathing*. Enough of this! ENOUGH! Guards! Attack and swarm them! I have a final plan! They can't win! THEY CAN'T!" (At the start of the death phase)
 * "I will not lose to simple-minded, simple weaponed, no side losers!" (Said randomly throughout death phase before reaching 0 health)
 * "This isn't the end! It can't be!" (Said randomly throughout death phase before reaching 0 health)
 * "My army is endless while you die away! SO JUST DIE!" (Said randomly throughout death phase before reaching 0 health)

"N-no... who will protect the squares now? Without me, tanks are free to kill all. Pathetic creatures! No sides! No hearts! No courage and all coward! I... I'm sorry mom... I have failed you..." *vaporized in white flash, only helmet and ash being left behind*

Trivia

 * Comparing Perpendiculus's personality to that of an overconfident 12-year-old's is very accurate.
 * Congratulations Da_Clorax for finding all 119 squares on this page (now it's 120 since I said it), any new words won't count anymore since it was a one-time event.
 * There are probably way more now.
 * Some attacks have square-related puns for names.
 * LAAAAAAAAG
 * Some attack summon absurd amounts of squares, which is why there's a limit on how many squares or square-related things that can be spawned during attacks (1400 total), unlike the other Polygon Disciples. However, that's still 70% of the amount of the theorized limit of squares (2000) in a vanilla Diep.io FFA or 2/4 Teams server.
 * Additionally, since Perpendiculus has a limit of 400 squares outside of his attacks, that still amounts to 2200 squares.
 * The Rightened Lightning attack was modified and is now slightly inspired by Elecman's attack from Megaman 1.
 * The rotated curved bracket that forms Perpendiculus's smile on his art is based on his Curtain of Steel art, which has the exact same smile.
 * Perpendiculus laughs his signature laugh every time a player dies, which is an annoying "HAW!" and during quotes. His bracket smile will also widen and curve upwards even more, even more if multiple players die within the span of a few seconds. It is purely aesthetic, mainly just to irritate his enemies.
 * Perpendiculus's battle room within his Stronghold part of his fortress is both square-shaped and substantially larger than those of the other Disciples' to make room for his beloved squares.
 * Additionally and ironically, despite his fortress having the most runes of all of the Polygon Fortresses, Perependiculus is the only Disciple illiterate in the ancient written language.