# Klipse Developer. Author. Speaker. This is one page of public article previews, not the complete archive. Follow Next page to continue. Summaries are not the original full articles. ## The Aboulafia Graph Has Dihedral Symmetry DevFeed: [The Aboulafia Graph Has Dihedral Symmetry]() Original publisher: [Read original article]() Author: Yehonathan Sharvit Published: 2026-07-06T10:00:00Z Content type: article Language: en Sources: [Klipse]() Topics: [Graphs]() Tags: [aboulafia](), [graph](), [math](), [mirror](), [rotation](), [series](), [symmetry]() ### AI overview The final article in a four-part series explains the dihedral symmetry of the Aboulafia graph. It connects the graph's recursive construction to a rotation and a reflection, and describes a proof that these are its only symmetries. ### Source excerpt Aboulafia's Tserouf - Part 4 of 4 <- Previous: Too big to draw, but yet drawable ## Too big to draw, but yet drawable DevFeed: [Too big to draw, but yet drawable]() Original publisher: [Read original article]() Author: Yehonathan Sharvit Published: 2026-07-06T09:00:00Z Content type: article Language: en Sources: [Klipse]() Topics: [ordering](), [structure]() Tags: [aboulafia](), [caustics](), [generative](), [math](), [permutation](), [permutations](), [random](), [ranking](), [recursion](), [visualization]() ### AI overview The third article in a series explains how Aboulafia's tserouf orders all permutations of a word and visualizes them by placing the permutations around a circle and connecting each word to its reversal. Because the full permutation space becomes too large to draw, the article samples chords and shows that they form recurring caustic curves visible at multiple scales. ### Source excerpt Aboulafia's Tserouf - Part 3 of 4 <- Previous: An elegant formulation, inspired by Bill Gates - Next: A wheel, the same forwards and backwards -> ## Zaks's suffix-reversal algorithm for generating permutations DevFeed: [Zaks's suffix-reversal algorithm for generating permutations]() Original publisher: [Read original article]() Author: Yehonathan Sharvit Published: 2026-07-06T08:00:00Z Content type: article Language: en Sources: [Klipse]() Topics: [Algorithm](), [Sorting](), [ordering]() Tags: [aboulafia](), [algorithm](), [math](), [permutations](), [reversing](), [sequence](), [sorting]() ### AI overview This second article in a series connects Aboulafia's recursive Tserouf permutation algorithm with Shimon Zaks's 1984 algorithm. It explains how Zaks generates permutations by repeatedly reversing suffixes and describes the recursive sequence of suffix lengths behind the ordering. ### Source excerpt Aboulafia's Tserouf - Part 2 of 4 <- Previous: An algorithm ignored for 700 years - Next: Too big to draw, but yet drawable -> ## A 13th-Century Enumeration Algorithm, Ignored for 700 Years DevFeed: [A 13th-Century Enumeration Algorithm, Ignored for 700 Years]() Original publisher: [Read original article]() Author: Yehonathan Sharvit Published: 2026-07-06T07:00:00Z Content type: article Language: en Sources: [Klipse]() Topics: [Algorithm](), [ordering](), [structure]() Tags: [aboulafia](), [algorithm](), [kabbalah](), [math](), [order](), [ordering](), [permutations]() ### AI overview The article examines a systematic method for enumerating permutations described by the 13th-century Kabbalist Abraham Aboulafia in his account of Tserouf. It explains rules for ordering three-letter permutations and a rotation-based method for extending the ordering to longer words. ### Source excerpt Aboulafia's Tserouf - Part 1 of 4 Next: An elegant formulation, inspired by Bill Gates -> ## Separate data schema from data representation DevFeed: [Separate data schema from data representation]() Original publisher: [Read original article]() Author: Yehonathan Sharvit Published: 2022-06-22T02:35:24Z Content type: article Language: en Sources: [Klipse]() Topics: [JSON Schema](), [Data validation](), [Programming]() Tags: [code](), [d](), [data-validation](), [dop](), [json-schema](), [programming]() ### AI overview An exploration of the fourth principle of Data-Oriented Programming: keeping data schemas separate from data representations. The article explains how schemas describe expected data shapes and how validation libraries such as Ajv can check data against JSON Schema and report validation errors. ### Source excerpt With data separated from code and represented with generic and immutable data structures, now comes the question of how do we express the shape of the data? In DOP, the expected shape is expressed as a data schema that is kept separated from the data itself. The main benefit of Principle #4 is that it allows developers to decide which pieces of data should have a schema and which pieces of data should not. ## Data is immutable DevFeed: [Data is immutable]() Original publisher: [Read original article]() Author: Yehonathan Sharvit Published: 2022-06-22T02:34:24Z Content type: article Language: en Sources: [Klipse]() Topics: [data](), [Programming](), [Data structures](), [Clojure](), [JavaScript]() Tags: [clojure](), [d](), [data](), [dop](), [immutability](), [javascript](), [mutation]() ### AI overview This article explains the third principle of Data-Oriented Programming: data is immutable. It describes replacing mutation with new data versions, contrasts this approach in Clojure and JavaScript, and discusses cloning and persistent data structures as implementation strategies. ### Source excerpt With data separated from code and represented with generic data structures, how are changes to the data managed? DOP is very strict on this question. Mutation of data is not allowed! In DOP, changes to data are accomplished by creating new versions of the data. The reference to a variable may be changed so that it refers to a new version of the data, but the value of the data itself must never change. ## Represent data with generic data structures DevFeed: [Represent data with generic data structures]() Original publisher: [Read original article]() Author: Yehonathan Sharvit Published: 2022-06-22T02:33:24Z Content type: article Language: en Sources: [Klipse]() Topics: [Data structures](), [Code](), [Programming](), [Object-oriented programming (OOP)](), [JavaScript]() Tags: [array](), [arrays](), [code](), [d](), [data-structures](), [dop](), [immutability](), [javascript](), [oop](), [programming]() ### AI overview This article explores the second principle of Data-Oriented Programming: representing application data with generic data structures such as maps and arrays instead of specific classes. It also discusses other structures, including sets, trees, and queues, and describes benefits such as reusable generic functions and a flexible data model. ### Source excerpt When adhering to Principle #1 of DOP, code is separated from data. DOP is not opinionated about the programming constructs to use for organizing the code, but it has a lot to say about how the data should be represented. This is the theme of Principle #2. ## Separate code from data DevFeed: [Separate code from data]() Original publisher: [Read original article]() Author: Yehonathan Sharvit Published: 2022-06-22T02:32:24Z Content type: tutorial Language: en Sources: [Klipse]() Topics: [Programming](), [Object-oriented programming (OOP)](), [classes]() Tags: [behavior](), [classes](), [code](), [d](), [data](), [dop](), [oop](), [programming]() ### AI overview This article explores the first principle of Data-Oriented Programming: separating code, or behavior, from data. It explains how the principle can be followed or violated in both object-oriented programming and functional programming, including examples involving classes, static methods, and lexical scope. ### Source excerpt The first principle of Data-Oriented Programming (DOP) is a design principle that recommends a clear separation between code (behavior) and data. This may appear to be a FP principle, but in fact, one can adhere to it or break it either in FP or in OOP: ## Principles of Data-Oriented Programming DevFeed: [Principles of Data-Oriented Programming]() Original publisher: [Read original article]() Author: Yehonathan Sharvit Published: 2022-06-22T02:31:24Z Content type: article Language: en Sources: [Klipse]() Topics: [data](), [Programming](), [Code](), [JavaScript](), [Functional programming](), [Object-oriented programming (OOP)]() Tags: [article](), [code](), [d](), [data](), [developer-experience](), [dop](), [javascript](), [programming]() ### AI overview This article explains the four core principles of Data-Oriented Programming: separating code from data, representing data with generic data structures, treating data as immutable, and separating data schemas from representations. It presents DOP as a language-agnostic approach intended to simplify software systems and improve developer experience. ### Source excerpt This article is an excerpt from my book about Data-Oriented Programming. More excerpts are available on my blog. ## An Experiment in Self-Referential Storytelling for Data-Oriented Programming DevFeed: [An Experiment in Self-Referential Storytelling for Data-Oriented Programming]() Original publisher: [Read original article]() Author: Yehonathan Sharvit Published: 2022-01-16T23:45:32Z Content type: opinion Language: en Sources: [Klipse]() Topics: [data](), [Programming]() Tags: [article](), [book](), [clojure](), [d](), [dop](), [programming]() ### AI overview The article describes an experiment involving self-referential storytelling in Chapter 13 of Data-Oriented Programming. Its fictional characters discover apparent parallels between their story and the book, including shared topics and character names. ### Source excerpt This is an experiment I am doing about introducing a bit of self-referential stuff in Chapter 13 of "Data-Oriented Programming.