Game keeps crashing when I try to open world

--- Minecraft Crash Report ----
// Surprise! Haha. Well, this is awkward.

Time: 2/9/13 8:56 AM
Description: Unexpected error

java.lang.OutOfMemoryError: Java heap space


A detailed walkthrough of the error, its code path and all known details is as follows:
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-- System Details --
Details:
	Minecraft Version: 1.4.7
	Operating System: Mac OS X (x86_64) version 10.7.5
	Java Version: 1.6.0_37, Apple Inc.
	Java VM Version: Java HotSpot(TM) 64-Bit Server VM (mixed mode), Apple Inc.
	Memory: 400176 bytes (0 MB) / 1060372480 bytes (1011 MB) up to 1060372480 bytes (1011 MB)
	JVM Flags: 3 total; -Xbootclasspath/a:/System/Library/PrivateFrameworks/JavaApplicationLauncher.framework/Resources/LauncherSupport.jar -Xms512M -Xmx1024M
	AABB Pool Size: 0 (0 bytes; 0 MB) allocated, 0 (0 bytes; 0 MB) used
	Suspicious classes: No suspicious classes found.
	IntCache: cache: 0, tcache: 0, allocated: 3, tallocated: 63
	LWJGL: 2.4.2
	OpenGL: ATI Radeon HD 6490M OpenGL Engine GL version 2.1 ATI-7.32.12, ATI Technologies Inc.
	Is Modded: Probably not. Jar signature remains and client brand is untouched.
	Type: Client (map_client.txt)
	Texture Pack: Default
	Profiler Position: N/A (disabled)
	Vec3 Pool Size: ~~ERROR~~ NullPointerException: null