Warning: "continue" targeting switch is equivalent to "break". Did you mean to use "continue 2"? in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/json/FormatJson.php on line 297

Deprecated: Optional parameter $prefix declared before required parameter $code is implicitly treated as a required parameter in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/languages/Language.php on line 4267

Deprecated: Return type of ResultWrapper::current() should either be compatible with Iterator::current(): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/DatabaseUtility.php on line 174

Deprecated: Return type of ResultWrapper::next() should either be compatible with Iterator::next(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/DatabaseUtility.php on line 192

Deprecated: Return type of ResultWrapper::key() should either be compatible with Iterator::key(): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/DatabaseUtility.php on line 185

Deprecated: Return type of ResultWrapper::valid() should either be compatible with Iterator::valid(): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/DatabaseUtility.php on line 202

Deprecated: Return type of ResultWrapper::rewind() should either be compatible with Iterator::rewind(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/DatabaseUtility.php on line 163

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: Return type of MediaWiki\Session\PHPSessionHandler::open($save_path, $session_name) should either be compatible with SessionHandlerInterface::open(string $path, string $name): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/session/PHPSessionHandler.php on line 172

Deprecated: Return type of MediaWiki\Session\PHPSessionHandler::close() should either be compatible with SessionHandlerInterface::close(): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/session/PHPSessionHandler.php on line 187

Deprecated: Return type of MediaWiki\Session\PHPSessionHandler::read($id) should either be compatible with SessionHandlerInterface::read(string $id): string|false, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/session/PHPSessionHandler.php on line 201

Deprecated: Return type of MediaWiki\Session\PHPSessionHandler::write($id, $dataStr) should either be compatible with SessionHandlerInterface::write(string $id, string $data): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/session/PHPSessionHandler.php on line 229

Deprecated: Return type of MediaWiki\Session\PHPSessionHandler::destroy($id) should either be compatible with SessionHandlerInterface::destroy(string $id): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/session/PHPSessionHandler.php on line 335

Deprecated: Return type of MediaWiki\Session\PHPSessionHandler::gc($maxlifetime) should either be compatible with SessionHandlerInterface::gc(int $max_lifetime): int|false, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/session/PHPSessionHandler.php on line 355

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: Return type of MediaWiki\Session\Session::count() should either be compatible with Countable::count(): int, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/session/Session.php on line 611

Deprecated: Return type of MediaWiki\Session\Session::current() should either be compatible with Iterator::current(): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/session/Session.php on line 616

Deprecated: Return type of MediaWiki\Session\Session::next() should either be compatible with Iterator::next(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/session/Session.php on line 626

Deprecated: Return type of MediaWiki\Session\Session::key() should either be compatible with Iterator::key(): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/session/Session.php on line 621

Deprecated: Return type of MediaWiki\Session\Session::valid() should either be compatible with Iterator::valid(): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/session/Session.php on line 636

Deprecated: Return type of MediaWiki\Session\Session::rewind() should either be compatible with Iterator::rewind(): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/session/Session.php on line 631

Deprecated: Return type of MediaWiki\Session\Session::offsetExists($offset) should either be compatible with ArrayAccess::offsetExists(mixed $offset): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/session/Session.php on line 645

Deprecated: Return type of & MediaWiki\Session\Session::offsetGet($offset) should either be compatible with ArrayAccess::offsetGet(mixed $offset): mixed, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/session/Session.php on line 657

Deprecated: Return type of MediaWiki\Session\Session::offsetSet($offset, $value) should either be compatible with ArrayAccess::offsetSet(mixed $offset, mixed $value): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/session/Session.php on line 666

Deprecated: Return type of MediaWiki\Session\Session::offsetUnset($offset) should either be compatible with ArrayAccess::offsetUnset(mixed $offset): void, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/session/Session.php on line 670

Warning: Private methods cannot be final as they are never overridden by other classes in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/actions/Action.php on line 67

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Warning: "continue" targeting switch is equivalent to "break". Did you mean to use "continue 2"? in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/languages/LanguageConverter.php on line 757

Deprecated: Message implements the Serializable interface, which is deprecated. Implement __serialize() and __unserialize() instead (or in addition, if support for old PHP versions is necessary) in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/Message.php on line 159

Deprecated: RawMessage implements the Serializable interface, which is deprecated. Implement __serialize() and __unserialize() instead (or in addition, if support for old PHP versions is necessary) in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/Message.php on line 1250

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: Optional parameter $label declared before required parameter $alt is implicitly treated as a required parameter in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/Linker.php on line 726

Deprecated: Optional parameter $label declared before required parameter $alt is implicitly treated as a required parameter in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/DummyLinker.php on line 144

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: header(): Passing null to parameter #3 ($response_code) of type int is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/WebResponse.php on line 42

Deprecated: header(): Passing null to parameter #3 ($response_code) of type int is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/WebResponse.php on line 42

Deprecated: header(): Passing null to parameter #3 ($response_code) of type int is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/WebResponse.php on line 42

Deprecated: header(): Passing null to parameter #3 ($response_code) of type int is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/WebResponse.php on line 42

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: trim(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/skins/SkinTemplate.php on line 354

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: Optional parameter $attribs declared before required parameter $contents is implicitly treated as a required parameter in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/Xml.php on line 131

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745

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</p><textarea readonly="" accesskey="," id="wpTextbox1" cols="80" rows="25" style="" lang="de" dir="ltr" name="wpTextbox1">== Reference ==
Javier Barrallo: [[Expanding the Mandelbrot Set into Higher Dimensions]]. In: [[Bridges 2010]]. Pages 247–254 

== DOI ==

== Abstract ==
When in 1980 Benoit Mandelbrot described the z→z^2+c formula, many mathematicians and programmers tried to
expand the Mandelbrot Set into the third dimension. But all of them where stopped by the non-equivalence in 3D to
the 2D complex product (a+bi)·(c+di), something that was well known since times of mathematician W. R.
Hamilton. Also, as the 80’s computers where not able to produce the calculations needed to represent an image of
that kind, all research moved towards other fractal fields. It was in 2007 when the search was recovered by means
of a controversial algorithm using algebra based on spherical coordinates triplets {ρ, φ, θ} (module, longitude and
latitude). Although, from a strict mathematical point of view, the process is not correct, the stunning images of the
3D set, especially when raised to higher polynomials z→zn+c soon became an iconic fractal named Mandelbulb.
The expansion of the Mandelbrot Set in 4D by means of quaternions is also possible. Recent experiments reveal
that adequate projecting surfaces provide an infinite group of projections into 3D.

== Extended Abstract ==

== Bibtex == 

== Used References ==
[1] Barrallo J. Fractal Geometry, 2nd ed. Editorial Anaya (Madrid). 1992.

[2] Hamilton W.R. Elements of Quaternions, 3rd ed. Chelsea Publishing Company. 1969.

[3] Douady A., Hubbard J.H. Iteration des polynomes quadratiques complexes. CRAS Paris 294, pp. 123-126. 1982.

[4] Hart J.C., Sandin D.J., Kauffman L.H., Ray tracing deterministic 3-D fractals. Computer Graphics (SIGGRAPH
’89 Proceedings) 23 (3), pp.289-296. 1989.

[5] Mandelbrot B.B. The Fractal Geometry of Nature, 2nd ed. Freeman. 1982.

[6] www.fractalforums.com - www.skytopia.com. Search for Mandelbulb section.


== Links ==
=== Full Text === 
http://archive.bridgesmathart.org/2010/bridges2010-247.pdf

[[intern file]]

=== Sonstige Links ===
http://archive.bridgesmathart.org/2010/bridges2010-247.html
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Deprecated: header(): Passing null to parameter #3 ($response_code) of type int is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/WebResponse.php on line 42

Deprecated: header(): Passing null to parameter #3 ($response_code) of type int is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/WebResponse.php on line 42

Deprecated: header(): Passing null to parameter #3 ($response_code) of type int is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/WebResponse.php on line 42

Deprecated: header(): Passing null to parameter #3 ($response_code) of type int is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/WebResponse.php on line 42

Deprecated: strlen(): Passing null to parameter #1 ($string) of type string is deprecated in /mnt/web618/b0/56/5203556/htdocs/mediawiki_01/includes/db/Database.php on line 1745