+ 
+ Microchip fractal mazes (2024 collection)
++ This page offers a selection of fractal mazes inspired by the works of Mark J. P. Wolf (2003) + and Ed Pegg Jr (2011). The collection starts with four hand-crafted mazes first published in + early 2021, now ported to PS+ and updated for faster game play. + The new set of designs for 2024 have been derived from computer-generated data provided by + Erich Friedman in late 2021, adapted to demonstrate a variety of new fractal maze-forms. +
+Use cursor-keys to move the spark along the wires, the spark will keep moving until it + reaches an unvisited goal or a decision point. Goals are indicated by orange squares and + can only be harvested on the home-level of the maze. Use ESC for level select.
+
+ Mazes 1-4: [2021] Bi-directional, single-goal, single-chip (the 2021 collection).
+ Mazes 2-?: [2024] Bi-directional, multi-goal, single-chip.
+ Mazes ?-?: [2024] Bi-directional, multi-goal, dual-chip.
+ Mazes ?-?: [2024] Bi-directional, multi-goal, split-chip.
+
+ Here is an image of... +
+
+ Development notes - History
+ +The Wolfram maze (2011) is an 8-pin maze, in a 22222/33 configuration. The 8 + edge-connectors (pins) offer 8 inner (downward) and 8 outer (upward) termini. + Of the 16 termini, 2 sets of 3 are connected to form the two decision points. + The other 10 termini are plumbed in 5 pairs with no decision points. + In 2011 I was intrigued by the depth of the recursion required to solve + such a minimal fractal design, but I also noted that if I could only + recurse outward from the start point I could reach the goal in a single move. +
+
+ In 2021 I eventually started exploring some bi-directional Wolfram-style mazes
+ of my own. I implemented them in rudimentary puzzlescript, and shared them at
+ itch.io. Later the same year Erich Friedman kindly started exploring other
+ configurations of 8 and 9 pin mazes, specifically configurations 22222/33 (8-pin)
+ through to 333333 (9-pin) with most effort spent on 22/3333 (8-pin).
+ The data taught me a lot about what was and wasn't possible with single-chip
+ fractal mazes. Ultimately provoking me to comment (in an email in
+ Jan 2022) that fractal mazes are endlessly fascinating in their ultimate
+ dullness!
. I needed to take a breather.
+ In Jan 2024 the dullness finally dissipated and I was tempted to take
+ another look at Erich's data, resulting in this, the 2024 collection.
+
Development notes - Implementation
+ +Puzzlescript is an ideal engine for implementing many grid-based logic-mazes, + however for fractal mazes it poses a few challenges. With no stack, and only + primitive mechanisms for counting how do you implement a potentially infinite + recursive maze? The short answer is... you don't. + Setting a generous (but finite) recursion limit avoids one set of problems, + but if a fractal shape can contain multiple copies of itself, then it is very + difficult to track current state without a stack. So to keep things simple + I decided to side-step the latter problem completely. Each + fractal chip is unique and contains a maximum of one copy of itself (or + another chip) following closely the simple model of the Wolfram maze.
+ +Development notes - clickmazes variations
+ +One key benefit of non-repetition of the fractal shape is there is no + ambiguity with recursing "upwards" from the start level, thus all mazes + featured here allow you to explore in both directions. But given this + restriction what other variations on the fractal maze are possible? Most of + the more complex fractal mazes you find online rely on repetition of + the same fractal shape within itself. + My first idea was to make the mazes multi-goal (by placing a separate + target on every home-level path). Then to start redistributing the + available microchip "pins" to form dual-chip and split-chip mazes. + Dual-chip mazes consists of two non-identical chips each containing a + copy of the other (to break parity direct connections between the dual-chips + are also permitted). + Split-chip is a further variation where the outer edge of the fractal + chip is an amalgamation of several non-identical inner chips. So 4 inner + chips, each with 3 outbound termini, yields an outer chip with 12 inbound + termini. These fractal mazes start to feel a little "cursed" but are they + fundamentally harder? Let me know if you decide. +
+ +Links and related pages
+ The Wolfram maze (Ed Pegg - 2011)
+ Mathpuzzle.com archive of the earliest fractal mazes (Mark J. P. Wolf - 2003)
+ Clickmazes Microchip fractal mazes V1 in PS (2021)
+ Solving Fractal mazes (freethoughtsblog)
+
+
+ concept - Mark J. P. Wolf - 2003
+ maze designs - © Andrea Gilbert and Erich Friedman 2021-24
+ puzzlescript implementation - © Andrea Gilbert - 2021-24
+
+
