Game of Life page element and built-in page

A new page element runs Conway's Game of Life in an area (the whole display
by default), one per page. Start: random dots, one pattern, or the icons
whose names start with a text in turn or in random order. Edges: wrap
around, dead, or a hidden margin where gliders fly out of view (leftovers
that stay put in the margin are cleared, so a glider gun runs cleanly).
It restarts when the board is still or repeats within 16 generations
and/or after a number of generations, after a hold time (an empty board
at once).

logic/life holds the board and timing (tested), display/life_player runs
the board of the shown page, ticked before each frame; frames are paced
like scrolling text. The element reuses existing fields, so the page
format stays the same. The Icons tab has a library of 17 LifeWiki
patterns (checked with a simulation), and the built-in page "Game of
Life" shuffles through the life_ icons. About 12 KB flash, 8 KB RAM.

Version 2.17.0, tested on the display over OTA.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

src/esp32/logic/page.cpp

@@ -7,6 +7,8 @@
 #include <string.h>
 #include <strings.h>
 
+#include "logic/life.h"
+
 static const uint16_t MINUTES_PER_DAY = 24 * 60;
 static const uint32_t MAX_TARGET = 36525UL * MINUTES_PER_DAY; // 2100-01-01
 
@@ -71,6 +73,13 @@ bool elementUsesHa(const PageElement &element)
 	}
 }
 
+bool sameLifeStart(const PageElement &a, const PageElement &b)
+{
+	return a.type == ElementType::Life && b.type == ElementType::Life && a.bar_width == b.bar_width &&
+		   a.bar_height == b.bar_height && a.format == b.format && a.input_unit == b.input_unit &&
+		   strcasecmp(a.text, b.text) == 0 && a.factor == b.factor && a.absolute == b.absolute;
+}
+
 bool pageUsesImage(const DynamicPage &page, const char *name, bool by_state)
 {
 	for (int i = 0; i < page.slot_count; i++)
@@ -79,6 +88,8 @@ bool pageUsesImage(const DynamicPage &page, const char *name, bool by_state)
 	for (int i = 0; i < page.element_count; i++)
 	{
 		const PageElement &e = page.elements[i];
+		if (e.type == ElementType::Life && e.input_unit == LIFE_START_PATTERN && sameName(e.text, name))
+			return true; // patterns to rotate through can be deleted (the list gets shorter)
 		if (e.type != ElementType::Image)
 			continue;
 		if (!e.entity[0])
@@ -152,11 +163,39 @@ static uint8_t formatCount(const PageElement &e)
 		return STOPWATCH_FORMAT_COUNT;
 	case ElementType::Bar:
 		return BAR_FORMAT_COUNT;
+	case ElementType::Life:
+		return LIFE_EDGES_COUNT;
 	default:
 		return 255; // not used
 	}
 }
 
+static const char *validateLife(const PageElement &e)
+{
+	if (e.bar_width < 1 || e.bar_width > BITMAP_WIDTH || e.bar_height < 1 || e.bar_height > BITMAP_HEIGHT)
+		return "Game of Life: width 1-84, height 1-19 dots";
+	if (e.input_unit >= LIFE_START_COUNT)
+		return "Game of Life: unknown start";
+	if (e.input_unit == LIFE_START_RANDOM && !(e.factor >= 1 && e.factor <= 100))
+		return "Game of Life: the density must be 1-100 %";
+	if (e.input_unit == LIFE_START_PATTERN && !validBitmapName(e.text))
+		return "Game of Life: choose a pattern";
+	if ((e.input_unit == LIFE_START_ROTATE || e.input_unit == LIFE_START_SHUFFLE) && e.text[0])
+	{
+		char name[ELEMENT_TEXT_SIZE + 1];
+		snprintf(name, sizeof(name), "%sx", e.text); // the start of a valid name
+		if (e.text[0] == ' ' || !validBitmapName(name))
+			return "Game of Life: invalid start of the pattern names";
+	}
+	if (!(e.scroll_speed >= LIFE_SPEED_MIN && e.scroll_speed <= LIFE_SPEED_MAX))
+		return "Game of Life: speed 0.1-20 generations per second";
+	if (e.target > LIFE_GENERATIONS_MAX)
+		return "Game of Life: at most 1000000 generations";
+	if (!(e.bar_max >= 0 && e.bar_max <= LIFE_HOLD_MAX))
+		return "Game of Life: hold 0-3600 seconds";
+	return nullptr;
+}
+
 const char *validatePage(const DynamicPage &page)
 {
 	if (page.slot_count > PAGE_SLOTS)
@@ -194,7 +233,7 @@ const char *validatePage(const DynamicPage &page)
 			return "Invalid entity or attribute";
 		if (e.decimals < DECIMALS_AS_IS || e.decimals > DECIMALS_MAX)
 			return "Decimals must be 0-4, or as received";
-		if (e.show >= HaShow::Count || e.input_unit >= UNIT_COUNT)
+		if (e.show >= HaShow::Count || (e.type != ElementType::Life && e.input_unit >= UNIT_COUNT))
 			return "Unknown Home Assistant value setting";
 		if (!printable(e.map, sizeof(e.map)))
 			return "The list of texts can only contain plain characters, up to 63";
@@ -218,6 +257,15 @@ const char *validatePage(const DynamicPage &page)
 			if (!isfinite(e.bar_max) || e.bar_max <= 0)
 				return "Progress bar: the full value must be a number above 0";
 		}
+		if (e.type == ElementType::Life)
+		{
+			const char *message = validateLife(e);
+			if (message)
+				return message;
+			for (int j = 0; j < i; j++)
+				if (page.elements[j].type == ElementType::Life)
+					return "A page can have one Game of Life";
+		}
 		if (e.type == ElementType::Countdown && e.target >= MAX_TARGET)
 			return "The countdown date must be before 2100";
 		if (e.type == ElementType::Image)
@@ -768,6 +816,7 @@ void elementText(const PageElement &e, const LocalTime &t, const ElementValues &
 		break;
 	case ElementType::Image:
 	case ElementType::Bar:
+	case ElementType::Life:
 		out[0] = '\0';
 		break;
 	default: