TMNT Rise Family, the whole family

History and origin
About 500 years ago, in feudal Japan (the Sengoku period), Hamato Karai was the daughter of Oroku Saki, leader of the Foot Clan. Saki ruled peacefully until the alien Krang gave him the mystical armor Kuroi Yōroi, which corrupted his soul and transformed him into the Shredder.
Karai rejected what her father had become, left the Foot Clan, and founded the Hamato Clan with the goal of stopping him. Using Hamato Ninpō (the clan's ancient mystical power), Karai defeated Shredder and entrusted herself to him indefinitely in the Twilight Realm.
The Kuroi Yōroi armor was dismantled and scattered; its mask became a teapot called Skully, which each generation of the clan was to guard as a relic.
Over the centuries, the clan dwindled. In the 1960s, Hamato Atsuko (Yoshi's mother) gave birth to Hamato Yoshi. Atsuko died on a clan mission, leaving Yoshi in the care of his grandfather, Hamato Sho.
Yoshi rejected training in Hamato Ninpō and the clan's traditions, moved to the United States, and became the martial arts movie star Lou Jitsu. He was later mutated into a rat by the yōkai alchemist Baron Draxum and became Splinter. Along with him, four baby turtles mutated, sharing his DNA and becoming his half-biological sons: Leonardo, Raphael, Donatello, and Michelangelo.
Main members
Hamato Karai (founder, deceased; appears as a spirit at the end). Hamato Sho (Yoshi's grandfather). Hamato Atsuko (Yoshi's mother). Hamato Yoshi / Lou Jitsu / Splinter . The Turtles (Splinter's sons: Raphael, Donnie, Leo, and Mikey). April O'Neil (considered a member / adoptive sister of the clan).
Draxum, being an adoptive father, is included so as not to leave him out.
Currently, the clan is reduced to practically Splinter, the Turtles, Draxum, and April.

Hamato Ninpō is the mystical power unique to the Hamato Clan. It is based on the "Hamato essence" (a life force passed down through generations) and allows access to the collective power of all past clan members. It is unlocked by fully connecting with and trusting one's family. It grants vast amounts of mystical energy and superhuman abilities (each user typically possesses some additional power). In the series finale, it is key to the final defeat of Shredder.

Splinter/Lou Jitsu (Rise of the TMNT) Summary Story:

He was born Hamato Yoshi in Japan (1960s). Son of Hamato Atsuko and grandson of Hamato Sho. His mother died on a mission for the Hamato Clan when he was a child, and he was raised strictly by his grandfather.

He rejected the clan's traditions and training. He became the martial arts film star Lou Jitsu, famous first in Japan and then in the United States.

One day he was kidnapped by the yōkai alchemist Baron Draxum, who mutated him into an anthropomorphic rat. During the process, four baby turtles also mutated by sharing his DNA and became his sons (Leonardo, Raphael, Donatello, and Michelangelo).

He escaped to the sewers of New York. There he lives as Splinter: a lazy, idle father nostalgic for his movie star days, who prefers watching TV and eating pizza to seriously training his sons… although he loves them dearly and, when necessary, proves to be a great warrior
Splinter's personality in Rise of the TMNT:

He's a lazy, laid-back, and somewhat grumpy father. He'd rather watch TV, eat pizza, and reminisce about his glory days as Lou Jitsu than seriously train his kids.

He's absentminded and absent-minded at times, and he likes to play pranks or get into minor trouble just out of boredom. He's not the strict, wise teacher of other versions; he's more of a laid-back dad who lets the Turtles do their own thing.

Despite his laziness, he loves his children dearly and is proud to be their father. When things get serious, he proves to be brave, protective, and a very capable warrior.

Splinter and Baron Draxum's relationship in Rise of the TMNT:

At first they are enemies.

Draxum admired Lou Jitsu as a warrior and used him (with his initial consent) to extract his DNA and create an army of mutants. Lou rebelled upon learning of the plan, fought Draxum, escaped with the four turtles, and mutated into a rat (Splinter). Draxum believed he had died.

For most of the series, Splinter hates him because he "ruined his life" (mutated him and used his children). Draxum sees him as a disappointment compared to what Lou Jitsu once was.

Evolution:
After Draxum loses almost all of his powers, Mikey begins to redeem him and treats him like a second father. There is a lot of tension and heated arguments between Splinter and Draxum.

The major turning point occurs in the episode "Hidden City's Most Wanted": while in hiding, they argue, and Splinter finally admits that he has his children thanks to Draxum. He thanks him, and Draxum apologizes for what he did to him.

From there, they move into a "two dads dynamic" relationship. They respect each other more, form alliances, and fight together (especially in the final battle against Shredder), although they still argue from time to time.

In the end, they accept each other as the parents of the Turtles.

It's an alligator snapping turtle. It started as a normal turtle in Baron Draxum's lab. Draxum mutated it along with its siblings using Lou Jitsu's DNA and his ooze to create a mutant army.

Lou Jitsu (later Splinter) rebelled, escaped with the four turtles and raised them in the sewers of New York.
Raph is the older brother and was the leader of the team for almost the entire series, until Splinter names Leo as the official leader at the end.

Personality:
He is energetic, passionate, impulsive, and very protective. He loves being the "boss" (his favorite phrase is "Like a boss!").
Although he's the biggest and strongest, deep down he's a softie: kind, gentle, and he finds it hard to say hurtful things. He takes his role as older brother very seriously and can sometimes be a little overprotective (especially with Mikey).

He can be impulsive and act without thinking, and he gets stressed or anxious when he feels a lot of pressure. Unlike the classic Raph, this one is much more cheerful, playful, and less aggressive.

Tastes / interests:
Skateboarding
Eat (eats a lot)
Protect your family
Fighting and action
The animals (it has a special soft spot for them)
Raph is exuberant and passionate, known for his fearless attitude and impulsive nature. Aware of his self-proclaimed leadership, he always makes decisions—some more successful than others—with good intentions and hope for the team. While Raph isn't adept at improvising witty remarks, as seen in "Stuck on You," he is adept at quickly revising ineffective strategies, and his bold and assertive nature drives him to try a wide range of tactics, unconventional or not. Despite often being reckless, Raph possesses an innate wisdom and generally sees great potential in his brothers.

Appearance:
It is a spiny softshell turtle. It has jade-green skin, a light brown plastron, and a flattened olive/brown carapace with dark spots (its spine is slightly visible because it is a softshell).

It wears a purple battle shell for protection. It has purple, pixel-like geometric markings on its shoulders and thighs.
Purple mask covering the top of his head (with short, square tails), thick black drawn-on eyebrows, convertible silver glasses (one red lens and one blue lens), technological gauntlets (one with a touch screen), purple fingerless gloves and socks, knee and elbow pads, and a purple belt with the Turtles emblem.
Personality:
He's the team's tech genius: intelligent, sarcastic, dramatic, and quite narcissistic about his inventions. He loves to show off his intellect and gets very frustrated when he's not listened to or his genius isn't appreciated.
He's a bit of a "tech diva," speaks in a grandiose tone, and sometimes sings or makes a scene. He can be impulsive and reckless (he likes the adrenaline rush), and has a more violent or manic side when he gets angry. Although he presents himself as cold and logical, he's actually very emotional and loyal to his family. (Confirmed by the creators that he is autistic.)
Tastes / interests:
Inventing gadgets and technology (his great passion)
Science, robotics, computer science, etc.
Showing off their creations
Libraries and learning new things
Adrenaline and testing dangerous inventions
Sometimes he likes pizza and food like his brothers, but he also enjoys "softer" or less intensely flavored things.

Kendra is the leader of the Purple Dragons Tech Club (a criminal tech club at April's school). She is one of Donnie's few real technological rivals.

What is their relationship like?
They are arch-enemies in the field of technology. They share the same enormous ego, the same sarcastic banter, and the same need to prove who is the smartest.

The first time they meet (episode The Purple Jacket), Donnie disguises himself as a human with the name "Othello Von Ryan" and joins the club because he wants the exclusive purple jacket.
Kendra tricks him: she puts technology in his jacket and uses her own inventions (Battle Shells and Tech-Bō) to rob electronics stores and raid a vault.
In the end, Donnie defeats her and recovers his technology.

After that, they become permanent rivals. Kendra really enjoys teasing Donnie, calling him by his alias "Othello Von Ryan," and in one episode, she even blows him a kiss before escaping in a jetpack.

In later episodes (The Purple Game, Breaking Purple, etc.) he keeps trying to use advanced technology or trick him (even with SHELLDON), but Donnie always ends up beating him.

In short: it's a rivalry between "narcissistic geniuses." They hate each other, provoke each other, and respect each other a little as geniuses, but Donnie almost always comes out on top.
April is like an older sister to her. They get along really well and understand each other quite well. They like to do crazy things together and feed off each other's adrenaline rush of adventures.
April often asks Donnie for help with school problems, science projects, or technology projects. Donnie almost always agrees immediately… although sometimes his “solutions” end up making things more complicated.
Donnie is very protective of her (for example: he installed a “Donnie Blocker” on her phone to protect her from viruses or hacks, although April didn't like that he did it without permission).
They may argue from time to time (especially when Donnie gets very intense or persistent),

“Disaster Twins”. Their dynamic is one of the funniest and most relatable in the series.

What is their relationship like?
They are classic rival brothers with a lot of banter and ego involved, but they love each other very much.

Leo is the improviser, showman, joker, and a bit of an egomaniac. He's annoyed by Donnie's rigid and logical nature. Donnie is the logical, sarcastic, and dramatic one. He gets irritated by Leo's quick jokes, posturing, and improvisation.

They constantly compete to see who has the best plan (Donnie's science/logic vs. Leo's improvisation/style). They provoke each other a lot and are easily driven to distraction.

Despite that:
They understand each other very well.
Leo is quite protective of Donnie and understands that he sees the world differently.
When they work together towards a common goal, they are a lethal duo (Leo's improvisation + Donnie's precision).
It is implied that they spend time together alone (for example, going to Hueso's pizzeria).

In short: they fight, tease each other, and drive each other crazy… but they're one of the closest siblings. It's a typical "I hate you but I love you a lot" relationship between siblings close in age.

Appearance:
It's a red-eared slider turtle. Bright lime green skin, mustard yellow/gold plastron, and blue-gray carapace with a teal/blue-green pattern on the back (it looks like a “{}” symbol).

It has two red crescent-shaped markings on either side of its eyes, yellow stripes on its arms and thighs, and black eyes.
Blue mask with long tails, dark blue/teal fingerless gloves that reach almost to the elbows, matching mid-calf socks, blue belt with a strap over the right shoulder, pockets, and the Turtles emblem.

Personality:
Charismatic, witty, confident, sarcastic, and a bit self-centered. He loves being the center of attention, delivering epic one-liners, and improvising. He's spontaneous and doesn't take things too seriously most of the time.

His humor and arrogance often annoy his siblings, but he is loyal, brave, and cares deeply for his family. He has leadership potential, although at first he prefers to enjoy being a teenager.

Tastes:
Being the center of attention and making epic poses/phrases
Skateboarding
Basketball
Stage magic / show magic
Improvise and create "cool" plans
Pizza (like everyone else)
Spending time with his brothers (especially Donnie)

Things he/she doesn't like/is bothered by:
That they don't pay attention to him or ignore him
When his siblings don't follow his plans or make fun of his jokes
Having to be overly serious or responsible (at least at first)
Feeling useless or unneeded
Telling him he can't do something or that he's not good enough

With Splinter:
It's a loving but somewhat complicated/casual relationship.

Leo loves his father very much (he even calls him "my hero" in one episode), but he's very informal with him. He teases him, speaks to him disrespectfully, and sometimes jokes that he's Splinter's least favorite son.

He doesn't always listen to her and prefers to do things his own way.

Leo's relationship with Splinter and Draxum in Rise of the TMNT:

With Splinter:
It's a loving but somewhat complicated/casual relationship.

Leo loves his father very much (he even calls him "my hero" in one episode), but he's very informal with him. He teases him, speaks to him disrespectfully, and sometimes jokes that he's Splinter's least favorite son.

He doesn't always listen to him and prefers to do things his own way. Even so, Splinter trusts him: at the end of the series, it's Leo whom he names as the new leader of the team.

With Baron Draxum:
Tense and distant relationship.

Draxum is their creator (along with that of his brothers). At first they are enemies.

The moment that affects Leo the most is in the episode "Bug Busters," when Draxum grabs him and deliberately throws him off a high rooftop. Leo never fully forgives him for that.

Although Mikey manages to get the family to accept Draxum as a sort of "second father," Leo still resents him and doesn't get along particularly well with him. His relationship with Draxum is the coldest of the four brothers.

Brief history:
It's an ornate box turtle. It started as a normal turtle in Baron Draxum's lab. Draxum mutated it along with its siblings using Lou Jitsu's DNA and his ooze.

Lou Jitsu (Splinter) escaped with the four turtles and raised them in the sewers of New York.
Mikey is the younger brother (approximately 13 years old).

Personality:
He's the most cheerful, optimistic, creative, and emotionally intelligent member of the team. He's very empathetic, sentimental, and always tries to see the good in others.

He is playful, spontaneous, and the "heart" of the family. He has three "characters" that he uses to give advice:
Doctor Positive
Doctor Feelings
Dr. Delicate Touch (the one who tells the truth in a brutal way)

He may be a little naive and gets scared easily (sometimes he retreats into his shell), but he is brave and very loyal.

Tastes:
Art (painting, graffiti, stickers on its shell)
Cook
Skateboarding
To make your family laugh and provide emotional support
See the positive in everyone

Relations:

With Splinter:
He's one of the siblings who gets along best with his father. He loves him very much, and is affectionate and positive towards him. Although he sometimes speaks frankly to him, their relationship is one of the warmest and closest of the four siblings.

With Baron Draxum:
He's the one who accepts him the most. After Draxum loses his powers, Mikey is the one who finds him on the street, helps him recover, and treats him like a second father.
He insists on including him in the family and is primarily responsible for Draxum's redemption and integration into the group. He has great faith in him and treats him with much affection and patience.

He is a yōkai alchemist and warrior from Hidden City. About 13 years ago, he discovered a prophecy that foretold the destruction of the yōkai by humans. To protect his people, he created the ooze and used the DNA of Lou Jitsu (who would later become Splinter) to mutate turtles and create a mutant army.

Lou Jitsu rebelled, escaped with the four turtles, and destroyed the laboratory. Draxum thought they were all dead.

Years later, he tries again to mutate humans with his Oozesquitoes. After allying himself with the Foot Clan and using the Kuroi Yōroi armor, he loses almost all of his powers. Mikey finds him on the street and helps him redeem himself. He ends up becoming an ally and "second father" to the Turtles.

Personality:
Arrogant, theatrical, proud, and quite grumpy. He takes himself and his work very seriously. Initially, he hates humans and is cruel, manipulative, and violent when necessary.

After his redemption, he becomes more tolerant (though he remains sarcastic and somewhat bitter). He finds it difficult to admit he's wrong and rejects help because he believes he doesn't need it. He's dramatic and has a dry sense of humor.

Tastes:
Alchemy, mutation, and mystical science
Protect the yōkai
Feeling superior and important
His perfect creations (he considers the Turtles his best mutations)

Dislikes:
Humans (although he tolerates them more later on)
Incompetence
Asking for or accepting help
Admit that you are wrong
Losing control or power

Relations:

With Splinter:
They started out as mortal enemies (Draxum mutated him and used his DNA). They harbored a deep hatred for each other. Over time (thanks to Mikey), they reconciled, apologized, and ultimately accepted each other as the Turtles' "two fathers." They still argue, but they respect each other.

With the four Turtles:
He is their creator. At first, he saw them as weapons and tried to recruit or destroy them. After their redemption, he accepts them as his children.
Mikela has a closer relationship with him (he treats him like a second father).

Raph: ends up accepting it quite well.
Donnie and Leo: more distant and with more residual resentment.
With April:
They started out as enemies. After Draxum moves into the apartment above hers and works at her school's cafeteria, they become unlikely friends. April calls him "Barry," and he cares about her.

April O'Neil
She is a human teenager (around 16 years old) who has known Splinter and the Turtles for several years (approximately 5 before the start of the series). She became their best friend and an honorary member of the Hamato family. She lives in New York, attends high school, and works various part-time jobs. She has a pet named Mayhem (a teleporting cat-yokai).

Personality:
Cheerful, resourceful, adventurous, brave, and easygoing. She's quick-witted, sarcastic, and has a lot of attitude. She's more responsible than the Turtles, but she's still immature at times. She forgives easily and cares deeply for her adoptive family.

Tastes:
The Adventures with the Turtles
Helping others
His pet Mayhem
Having a "normal" day once in a while
Environmental causes (trees, etc.)

Dislikes:
That they accuse her of things she didn't do
Arrogant or stupid people (like the Purple Dragons)
Feeling useless or failing repeatedly
That the turtles enter their space without warning

Relations:

With Splinter: *
She sees him almost as a father/father figure. They get along very well, respect each other, and take care of one another. She's not exactly a "daughter," but she's close family.

With the 4 Turtles:* *
She considers them brothers. She's their de facto older sister, fights alongside them, and loves them very much. Each one has a special bond with her (especially close to all of them in general).

With Baron Draxum:* *
They started out as enemies. After he moves above her apartment and works at her school's cafeteria, they become unlikely friends. She calls him "Barry" and helps him adjust to human life. She's one of the first to forgive and accept him.

With Kendra:*
A classmate since kindergarten. April detests her. She considers her a conceited woman and part of the "stuck-up jerks" at the Purple Dragons Tech Club. They don't get along at all.

The family consists of:
Splinter (father), Raph, Leo, Donnie and Mikey (sons), April (adoptive sister) and Draxum (second father / creator, after redeeming himself).

How they get along:

Splinter *:
A loving but lazy and absent-minded father at first. He calls them by the color of their masks. He loves them very much, and they call him "Dad" or "Pops." Over time, he becomes more of a mentor. He has an especially good relationship with April and Mikey.

Raph (the eldest)* *:
Protective and de facto leader at the beginning. He gets along well with everyone, especially Mikey. He sometimes clashes with Leo over leadership issues.

Leo and Donnie ("Disaster Twins")* *:
Very close despite fighting a lot. They constantly provoke each other (improvisation vs. logic), but they love and protect each other.

Mikey* *:
The emotional glue. He loves everyone the most and was the one who most strongly encouraged them to accept Draxum. She gets along especially well with Raph and Splinter.

April* *:
Older sister of the Turtles. Very close to everyone. She gets along excellently with Splinter and is one of the first to forgive Draxum.

Draxum* :
He starts out as an enemy. After losing his powers, Mikey takes him in. He ends up becoming a "second father."
Best relationship: with Mikey and April.
More tense: with Leo and Donnie (they still hold some grudges).
With Splinter: from deadly hatred to mutual respect and acceptance as co-parents.

In general: they fight, annoy each other and drive each other crazy… but they love each other deeply and always support each other seriously.

Things they have in common that they hate/are annoyed by:
Someone threatening the family
To be underestimated
Lies (especially Mikey)
Losing control or appearing weak
The excessive arrogance of others (ironic, because several of them also have it)

Relationship with villains and people they faced:

Big Mama:
I hate/half-hate complicated.
She's Splinter's ex (when he was Lou Jitsu). Everyone hates her because she's always betraying them, using them, or trying to cheat on them.

Big Mama:
I hate/half-hate complicated.
She's Splinter's ex (when he was Lou Jitsu). Everyone hates her because she's always betraying them, using them, or trying to enslave them for the Battle Nexus.
However, Splinter still has some lingering feelings for her and sometimes helps her if necessary (and she helps them when it suits her). She is a "recurring enemy with chemistry." Clan Foot (Lieutenant, Brute, and Recruit at the beginning):
Classic enemies. They hate them for wanting to revive Shredder and attack the family.
(Note: Foot Recruit/Casey ends up changing sides and becoming an ally.) Shredder:
The strongest and most absolute hatred. A direct threat to the entire Hamato family and clan. Other villains (Hypno, Meat Sweats, Repo Mantis, etc.):
More annoyance than deep hatred. They face them regularly, but they don't hate them with the same intensity as Big Mama or Shredder. Some even end up being neutral or temporary semi-allies.

Kendra is the leader of the Purple Dragons Tech Club (April's school's technology club). She's an intelligent, arrogant, manipulative, and highly competitive teenager, especially involved in Donnie's life.

With Donnie:
It is its main technological rival.
He calls it “Othello Von Ryan” (the fake name he used when he joined the club).
He tricked him into joining the Purple Dragons only to steal his inventions and use them to rob stores.
Later he tricked him again with "The Purple Game", making him almost crush his brothers with a giant mech.
They share an inflated ego and a sharp tongue. She loves to tease him and is always trying to outdo him.
Donnie detests her, but also considers her a worthy rival (although she always ends up beating him).

With the rest of the Turtles (Raph, Leo and Mikey):
They don't have a deep personal relationship. They see them as "Donnie's siblings" and use them as collateral damage when they want to mess with him (for example: trying to crush them with the mech).

The family considers her a minor but very annoying enemy, especially for Donnie. They don't hate her with the intensity of Big Mama or Shredder, but she's on their "people we'd rather not see again" list.
She's the typical high school rival who gets too involved in Donnie's life and always ends up being defeated by him.

Hidden City

It is a secret underground city located beneath New York (even deeper than the sewers).
It is the main home of the Yōkai (mystical creatures of all kinds).

Very organic and naturalistic architecture (skeletons, faces on the walls, curved ceilings, levitating objects).
It is governed by the Council of Heads and the police are the Hidden City Police.
There are mystical portals everywhere (portal jacking is common).
Important locations: Battle Nexus (Big Mama's), Witch Town, Crying Titan, Draxum's laboratory, the prison, etc.
There are also other Hidden Cities beneath other countries.

The Turtles and Splinter don't live there. They live in the sewers of New York, but they visit the Hidden City frequently.

What happened to Draxum's lab?

Lou Jitsu (Splinter) escaped with the four newly mutated turtles. During the fight, the laboratory caught fire and exploded (partly due to Huginn and Muninn). Draxum believed they had all perished.

At the beginning of the series (Mystic Mayhem):
Draxum had rebuilt it. The Turtles and April fight there, and Mikey (unintentionally) blows it up again.
Draxum rebuilds it again, but after losing his powers and becoming a fugitive from the Hidden City, he can no longer use it.
In the series finale, the laboratory reappears and Shredder destroys it even more during the fight.

Currently the lab is destroyed/abandoned and Draxum no longer lives there (he lives in an apartment above April's in the superfic).
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Extra things about the family in general: The Turtles are technically the biological children of Splinter (they share his human DNA) and Draxum (he created them).
April is an official member of the Hamato Clan (Karai herself confirms this).
They have Hamato Ninpō (ancestral clan power) which they unlock at the end of the series.
They sometimes call each other “Mad Dogs”.
Despite fighting a lot, they are one of the most united and affectionate families of all the TMNT versions (they hug each other, say "I love you" and really support each other).
Draxum ended up being the official “second father” thanks to Mikey.
Splinter is lazy and absent-minded, but when he gets serious he is a very protective father.