diff --git a/lib/pages/creature-page/core.tsx b/lib/pages/creature-page/core.tsx
index facb0d9..66b2dcc 100644
--- a/lib/pages/creature-page/core.tsx
+++ b/lib/pages/creature-page/core.tsx
@@ -42,6 +42,7 @@ import { VocabularyWidget } from "../../vocabulary-widget";
 import { createDistribution } from "../../distribution";
 import { ComponentWithShareableStateProps } from "../../page-with-shareable-state";
 import { useDebouncedEffect } from "../../use-debounced-effect";
+import { useRememberedState } from "../../use-remembered-state";
 
 /**
  * The minimum number of attachment points that any symbol used as the main body
@@ -264,9 +265,15 @@ export const CreaturePageWithDefaults: React.FC<
   ComponentWithShareableStateProps<CreatureDesign>
 > = ({ defaults, onChange }) => {
   const svgRef = useRef<SVGSVGElement>(null);
-  const [randomlyInvert, setRandomlyInvert] = useState(true);
+  const [randomlyInvert, setRandomlyInvert] = useRememberedState(
+    "creature-page:randomlyInvert",
+    true
+  );
   const [compCtx, setCompCtx] = useState(defaults.compCtx);
-  const [complexity, setComplexity] = useState(INITIAL_COMPLEXITY_LEVEL);
+  const [complexity, setComplexity] = useRememberedState(
+    "creature-page:complexity",
+    INITIAL_COMPLEXITY_LEVEL
+  );
   const [creature, setCreature] = useState(defaults.creature);
   const defaultCtx = useContext(CreatureContext);
   const newRandomCreature = () => {
@@ -286,7 +293,8 @@ export const CreaturePageWithDefaults: React.FC<
     ...defaultCtx,
     ...compCtx,
   });
-  const [alwaysInclude, setAlwaysInclude] = useState<SvgSymbolData>(
+  const [alwaysInclude, setAlwaysInclude] = useRememberedState<SvgSymbolData>(
+    "creature-page:alwaysInclude",
     EMPTY_SVG_SYMBOL_DATA
   );
   const design: CreatureDesign = useMemo(
diff --git a/lib/randomizer-widget.tsx b/lib/randomizer-widget.tsx
index 03cd583..55ed533 100644
--- a/lib/randomizer-widget.tsx
+++ b/lib/randomizer-widget.tsx
@@ -1,4 +1,4 @@
-import React, { useState } from "react";
+import React from "react";
 import { PaletteAlgorithmWidget } from "./palette-algorithm-widget";
 import { Random } from "./random";
 import {
@@ -7,6 +7,7 @@ import {
   RandomPaletteAlgorithm,
 } from "./random-colors";
 import { SvgCompositionContext } from "./svg-composition-context";
+import { useRememberedState } from "./use-remembered-state";
 
 type SvgCompositionColors = Pick<
   SvgCompositionContext,
@@ -31,10 +32,15 @@ export type RandomizerWidgetProps = {
 
 export const RandomizerWidget: React.FC<RandomizerWidgetProps> = (props) => {
   type RandType = "colors" | "symbols" | "colors and symbols";
-  const [paletteAlg, setPaletteAlg] = useState<RandomPaletteAlgorithm>(
-    DEFAULT_RANDOM_PALETTE_ALGORITHM
+  const [paletteAlg, setPaletteAlg] =
+    useRememberedState<RandomPaletteAlgorithm>(
+      "randomizer-widget:paletteAlg",
+      DEFAULT_RANDOM_PALETTE_ALGORITHM
+    );
+  const [randType, setRandType] = useRememberedState<RandType>(
+    "randomizer-widget:randType",
+    "colors and symbols"
   );
-  const [randType, setRandType] = useState<RandType>("colors and symbols");
   const randomize = () => {
     if (randType === "colors" || randType === "colors and symbols") {
       props.onColorsChange(createRandomCompositionColors(paletteAlg));
diff --git a/lib/use-remembered-state.ts b/lib/use-remembered-state.ts
new file mode 100644
index 0000000..0dd386a
--- /dev/null
+++ b/lib/use-remembered-state.ts
@@ -0,0 +1,39 @@
+import { useCallback, useState } from "react";
+
+/**
+ * This is where we remember the most recently-set values
+ * for `useRememberedState`.
+ */
+const shortTermMemory = new Map<string, any>();
+
+/**
+ * This is like React's `useState()`, but it also takes a "key" which
+ * uniquely identifies the state's value globally across the whole
+ * application.
+ *
+ * The most recent value is always remembered for the lifetime of the
+ * current application (but not across page reloads) and is returned
+ * instead of the initial state if possible.
+ *
+ * This effectively allows us to have user interface elements that
+ * "remember" their most recent value, even if the UI itself was
+ * unmounted at some point.
+ */
+export function useRememberedState<S>(
+  key: string,
+  initialState: S | (() => S)
+): [S, (value: S) => void] {
+  const remembered = shortTermMemory.get(key);
+  const [value, rawSetValue] = useState<S>(
+    remembered === undefined ? initialState : remembered
+  );
+  const setValue = useCallback(
+    (value: S) => {
+      shortTermMemory.set(key, value);
+      rawSetValue(value);
+    },
+    [key, rawSetValue]
+  );
+
+  return [value, setValue];
+}