Game maxes out memory, then crashes

I was making a large map, a 3x3 grid, as I explored the maps to reveal them the game maxed out memory and crashed. This has happened to me 3 times already.

What I expected to happen was the memory would be cleared as I explored the world to allow for more chunks and such to load, letting more of the maps be revealed.

What actually happened was was the memory maxed, teetered between 96-100%, then crashed.

Steps to reproduce
1. Create several large maps 2048 blocks apart.
2. Start revealing maps
3. Memory usage teeters between 96-100%
4. Reveal maps for an hour to two hours at least.
*During last crash music attempted to play. On second crash music was turned off however.

Edit:
Here is the Crash Report:

Minecraft Crash Report ----
// Don't do that.

Time: 2/2/14 3:39 AM
Description: Exception in server tick loop

java.lang.OutOfMemoryError: Java heap space

A detailed walkthrough of the error, its code path and all known details is as follows:
---------------------------------------------------------------------------------------

– System Details –
Details:
Minecraft Version: 1.7.4
Operating System: Windows 7 (x86) version 6.1
Java Version: 1.7.0_51, Oracle Corporation
Java VM Version: Java HotSpot(TM) Client VM (mixed mode, sharing), Oracle Corporation
Memory: 81472 bytes (0 MB) / 518979584 bytes (494 MB) up to 518979584 bytes (494 MB)
JVM Flags: 2 total; -XX:HeapDumpPath=MojangTricksIntelDriversForPerformance_javaw.exe_minecraft.exe.heapdump -Xmx512M
AABB Pool Size: 7740 (433440 bytes; 0 MB) allocated, 0 (0 bytes; 0 MB) used
IntCache: cache: 0, tcache: 0, allocated: 12, tallocated: 94
Profiler Position: N/A (disabled)
Vec3 Pool Size: 996 (55776 bytes; 0 MB) allocated, 0 (0 bytes; 0 MB) used
Player Count: 1 / 8; [mp['The_endeavorer'/209, l='Really Interesting', x=-213.62, y=172.10, z=-2831.63]]
Type: Integrated Server (map_client.txt)
Is Modded: Probably not. Jar signature remains and both client + server brands are untouched.