[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-84623-en":3,"doc-seo-84623-105":28,"detail-sidebar-cat-0-en-105":89},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":11,"language":21,"language_code":22,"site_id":23,"html_lang":22,"table_of_contents":24,"faqs":25,"seo_title":13,"seo_description":14,"update_tm":26,"read_time":27},84623,1649267921044,"Ava Thompson","https://us-avatar.wpscdn.com/avatar/1800007509477c92dfb?_k=1782875107921204101",8,"Research & Report","BFF Simple explanations for complex phenomena","BFF investigates how self-replicators can emerge in a computational soup when programs are evolved and executed as short fixed-length tapes interpreted as Brainfuck dialect code. Instead of relying on paired interactions, the work tests an alternate approach: simple mutation random walks in program space, supported by self-replicator detection methods. Results show distributionally tuned random mutation can match pairwise interactions for finding self-replicators, while limiting ancestry-tree depth/width restricts takeover rather than preventing emergence.","arXiv :2607 .0 1483v 1 [ cs .NE] 1 Jul 2026  \nBFF: Simple explanations for complex phenomena Charlotte Knierim, Luca Versari, Robert Obryk, Blaise Agüera y Arcas, Rif A. Saurous  \nGoogle, Paradigms of Intelligence Team  \nJuly 3, 2026  \nAbstract  \nThe “Computational Life” paper (Agüera y Arcas et al., 2024) argues that paired interactions in a computational soup are an effective way to find self-replicators. In this work, aided by recent developments in self-replicator detection, we explore the alternate hypothesis that self-replicators can be found at least as easily using simple mutation random walks in program space. We also explore the claim that capping the maximum “depth” and “width” of the ancestry tree stops self-replicators from emerging, showing instead that it merely stops self-replicators from taking over the soup.  \n1 Introduction  \nIn the “Computational Life” paper (Agüera y Arcas et al., 2024), self-replicators were detected by observing that they had “taken over” a computational soup. We observed this transition by measuring the size of a compressed version of the soup, which rapidly becomes significantly smaller as a self-replicator takes over the soup. In the interim, we have developed (reasonably) reliable direct self-replicator detectors. These detectors allow us to disentangle the initial appearance of self-replicators, which occurs in system with random mutation alone as well as ones with program interaction alone, and their widespread diffusion through the soup, which requires program interaction.  \nThe work presented here suggests that, in BFF, distributionally tuned random mutation is at least as powerful as pairwise interactions for finding self-replicators, and potentially for evolving programs with specific purposes.  \n1.1 Overview  \nThe BFF system consists of a soup of random strings of length 64 (also called tapes) . Those tapes are interpreted as programs in BFF, a dialect of the Brainfuck language [5] . The I/O in BFF works via two heads that also sit on the tape, meaning that programs can modify themselves while they run.  \nThe system runs by repeatedly choosing two programs uniformly at random, concatenating them and running the result, length 128, as if it were a single program.1 After execution, the tapes are taken apart and the two pieces are placed back into the soup in their new state.  \nNote that we have seen many different variants of BFF: different ways to map bytes to ops, slightly different operator sets, different soup sizes, interactions with all programs paired up simultaneously or one interaction at a time. This document aims to be generic in the BFF dialect; we repeated the experiments for multiple variants, with very similar results. The main variant we use, bff_selfmove [3], only has one copy operation and automatically moves the read head on a copy.  \n1.2 Main Results  \nOur primary finding is that we can easily find BFF self-replicators by executing a simple “random walk mutation” process in program space faster than we can find them by evolving the soup via paired computation.  \n1We have an upper bound on the number of steps in case the resulting program has an infinite loop.  \nWe measure time according to the number of programs seen during the process, and observe faster selfreplicator emergence.  \nStatistics on the number of self-replicators in other computational systems and parallels to biology have been explored in [4] .  \nMore generally, these experiments support the view that program interaction in BFF (or similar systems involving the dyadic interaction of short fixed-length tapes) is not an unusually powerful search operator. We continue to believe, for substantial theoretical and empirical reasons, that biology makes powerful use of recombination (both standard crossover and horizontal gene transfer (HGT)) . However, we do not currently consider program interaction in BFF to be an effective model of these processes. Finding good computational instantiations of cross","cbCaioXQjoCffwFv","https://ap.wps.com/l/cbCaioXQjoCffwFv","pdf",1254196,1,"English","en",105,"# Introduction\n## Overview\n## Main Results\n# Self-replication detector","[{\"question\":\"How does BFF execute programs in the computational soup?\",\"answer\":\"BFF repeatedly selects two programs at random, concatenates them, executes the length-128 result, then splits the tapes and returns the modified pieces to the soup.\"},{\"question\":\"What method does the document use to find self-replicators?\",\"answer\":\"It uses a self-replication detector that checks whether a program produces children matching its own behavior and structure, accounting for variants such as partial byte copying and parity-dependent self-inversion.\"},{\"question\":\"What key finding does the work report about search operators?\",\"answer\":\"Distributionally tuned random mutation in program space can be at least as powerful as paired program interactions for finding BFF self-replicators.\"}]",1784197220,20,{"code":4,"msg":29,"data":30},"ok",{"site_id":23,"language":22,"slug":31,"title":13,"keywords":32,"description":14,"schema_data":33,"social_meta":84,"head_meta":86,"extra_data":88,"updated_unix":26},"bff-simple-explanations-for-complex-phenomena","",{"@graph":34,"@context":83},[35,52,66],{"@type":36,"itemListElement":37},"BreadcrumbList",[38,42,46,49],{"item":39,"name":40,"@type":41,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":43,"name":44,"@type":41,"position":45},"https://docshare.wps.com/document/","Document",2,{"item":47,"name":12,"@type":41,"position":48},"https://docshare.wps.com/document/research-report/",3,{"item":50,"name":13,"@type":41,"position":51},"https://docshare.wps.com/document/bff-simple-explanations-for-complex-phenomena/84623/",4,{"url":50,"name":13,"@type":53,"author":54,"headline":13,"publisher":56,"fileFormat":59,"inLanguage":22,"description":14,"dateModified":60,"datePublished":60,"encodingFormat":59,"isAccessibleForFree":61,"interactionStatistic":62},"DigitalDocument",{"name":9,"@type":55},"Person",{"url":39,"name":57,"@type":58},"DocShare","Organization","application/pdf","2026-07-16",true,{"@type":63,"interactionType":64,"userInteractionCount":4},"InteractionCounter",{"@type":65},"ViewAction",{"@type":67,"mainEntity":68},"FAQPage",[69,75,79],{"name":70,"@type":71,"acceptedAnswer":72},"How does BFF execute programs in the computational soup?","Question",{"text":73,"@type":74},"BFF repeatedly selects two programs at random, concatenates them, executes the length-128 result, then splits the tapes and returns the modified pieces to the soup.","Answer",{"name":76,"@type":71,"acceptedAnswer":77},"What method does the document use to find self-replicators?",{"text":78,"@type":74},"It uses a self-replication detector that checks whether a program produces children matching its own behavior and structure, accounting for variants such as partial byte copying and parity-dependent self-inversion.",{"name":80,"@type":71,"acceptedAnswer":81},"What key finding does the work report about search operators?",{"text":82,"@type":74},"Distributionally tuned random mutation in program space can be at least as powerful as paired program interactions for finding BFF self-replicators.","https://schema.org",{"og:url":50,"og:type":85,"og:title":13,"og:site_name":57,"og:description":14},"article",{"robots":87,"canonical":50},"index,follow",{"doc_id":7,"site_id":23},{"code":4,"msg":5,"data":90},[91,95,99,103,108,113,118,121,125,128,132],{"id":20,"doc_module":4,"doc_module_name":44,"category_name":92,"show_sort_weight":93,"slug":94},"Story & Novel",90,"story-novel",{"id":45,"doc_module":4,"doc_module_name":44,"category_name":96,"show_sort_weight":97,"slug":98},"Literature",80,"literature",{"id":51,"doc_module":4,"doc_module_name":44,"category_name":100,"show_sort_weight":101,"slug":102},"Exam",70,"exam",{"id":104,"doc_module":4,"doc_module_name":44,"category_name":105,"show_sort_weight":106,"slug":107},5,"Comic",60,"comic",{"id":109,"doc_module":4,"doc_module_name":44,"category_name":110,"show_sort_weight":111,"slug":112},6,"Technology",50,"technology",{"id":114,"doc_module":4,"doc_module_name":44,"category_name":115,"show_sort_weight":116,"slug":117},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":44,"category_name":12,"show_sort_weight":119,"slug":120},30,"research-report",{"id":122,"doc_module":4,"doc_module_name":44,"category_name":123,"show_sort_weight":27,"slug":124},9,"Religion & Spirituality","religion-spirituality",{"id":27,"doc_module":4,"doc_module_name":44,"category_name":126,"show_sort_weight":27,"slug":127},"World Cup","world-cup",{"id":129,"doc_module":4,"doc_module_name":44,"category_name":130,"show_sort_weight":129,"slug":131},10,"Lifestyle","lifestyle",{"id":133,"doc_module":4,"doc_module_name":44,"category_name":134,"show_sort_weight":104,"slug":135},19,"General","general"]