{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/lenia-and-expanded-universe","title":"Lenia and Expanded Universe","arxiv_id":"2005.03742","date":"2020-05-07","proceeding":null,"authors":["Bert Wang-Chak Chan"],"abstract":"We report experimental extensions of Lenia, a continuous cellular automata family capable of producing lifelike self-organizing autonomous patterns. The rule of Lenia was generalized into higher dimensions, multiple kernels, and multiple channels. The final architecture approaches what can be seen as a recurrent convolutional neural network. Using semi-automatic search e.g. genetic algorithm, we discovered new phenomena like polyhedral symmetries, individuality, self-replication, emission, growth by ingestion, and saw the emergence of \"virtual eukaryotes\" that possess internal division of labor and type differentiation. We discuss the results in the contexts of biology, artificial life, and artificial intelligence.","url_abs":"https://arxiv.org/abs/2005.03742v1","url_pdf":"https://arxiv.org/pdf/2005.03742v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"lenia-and-expanded-universe","repo_url":"https://github.com/Chakazul/Lenia","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"lenia-and-expanded-universe","repo_url":"https://github.com/morgangiraud/leniax","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"jax","reach":null}],"tasks":[{"task_slug":"artificial-life","task_name":"Artificial Life"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=2005.03742","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"2005.03742"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. Samples come from repositories linked to the paper, official or community; repo_kind says which.","repos":[{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/morgangiraud/leniax","reach":null},{"provenance":"external:paperswithcode_snapshot_2025-07-28","url":"https://github.com/Chakazul/Lenia","reach":{"status":"ok","spdx":"MIT"}}],"summary":{"ran_draft_wrong":1,"ran_fixture":1,"ran_violates":2,"unverified":1},"by_repo_kind":{},"repo_kind_vocabulary":{"official":"The archive marks this repository official for the paper","named_in_paper":"The archive records that the paper mentions this repository; it is not marked official","listed":"In the archive's code links for this paper, not marked official and not recorded as mentioned in the paper","found_in_text":"Syntology found this repository in the paper's own text; whether it is the authors' implementation is not asserted","community":"Not in the archive's code links for this paper; a community repository Syntology harvested"},"n_pointer_only_for_licence":5,"samples":[{"code_sha256_prefix":"2cd391ee118a3067","entry":"K_init","repo":null,"repo_kind":null,"path":null,"file_url":null,"link_basis":"identical_code_first_harvested_elsewhere","language":"python","status":"ran_draft_wrong","verification_level":1,"contract_check":"MISDECLARED","metamorphic_tier":"invariant","behaviour_fingerprint":false,"licence":null,"inline_ok":false,"mcp_get_code":{"code_sha256":"2cd391ee118a3067"}},{"code_sha256_prefix":"f6d741560c3af1b4","entry":"all_states_loss_fn","repo":null,"repo_kind":null,"path":null,"file_url":null,"link_basis":"identical_code_first_harvested_elsewhere","language":"python","status":"ran_fixture","verification_level":1,"contract_check":"RAISES","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":null,"inline_ok":false,"mcp_get_code":{"code_sha256":"f6d741560c3af1b4"}},{"code_sha256_prefix":"36ba4775a42b57fd","entry":"linear_scale","repo":null,"repo_kind":null,"path":null,"file_url":null,"link_basis":"identical_code_first_harvested_elsewhere","language":"python","status":"ran_violates","verification_level":1,"contract_check":"VIOLATES","metamorphic_tier":"well_formed","behaviour_fingerprint":true,"licence":null,"inline_ok":false,"mcp_get_code":{"code_sha256":"36ba4775a42b57fd"}},{"code_sha256_prefix":"f61f86e94fe1db4f","entry":"update_config","repo":null,"repo_kind":null,"path":null,"file_url":null,"link_basis":"identical_code_first_harvested_elsewhere","language":"python","status":"ran_violates","verification_level":1,"contract_check":"VIOLATES","metamorphic_tier":"deterministic","behaviour_fingerprint":false,"licence":null,"inline_ok":false,"mcp_get_code":{"code_sha256":"f61f86e94fe1db4f"}},{"code_sha256_prefix":"36a8f94d44dd29bb","entry":"get_update_config","repo":null,"repo_kind":null,"path":null,"file_url":null,"link_basis":"identical_code_first_harvested_elsewhere","language":"python","status":"unverified","verification_level":0,"contract_check":null,"metamorphic_tier":null,"behaviour_fingerprint":false,"licence":null,"inline_ok":false,"mcp_get_code":{"code_sha256":"36a8f94d44dd29bb"}}]},"arxiv_metadata":null,"syntology_extracted_results":null}