Minecraft constantly crashes [duplicate]

Unlike everyone elses problems! Mine crashes after I've logged on; at the part that says: "Mojang".

I had mods installed but have since removed them completely and it still isn't working.

Below I've attached the minecraft crash report:

---- Minecraft Crash Report ----
// My bad.

Time: 7/20/15 9:27 PM
Description: Initializing game

java.lang.OutOfMemoryError: Java heap space
    at bmi.a(SourceFile:230)
    at bmh.b(SourceFile:130)
    at bmh.a(SourceFile:77)
    at bot.j(SourceFile:553)
    at bot.a(SourceFile:139)
    at bou.a(SourceFile:23)
    at bnn.a(SourceFile:99)
    at ave.am(SourceFile:448)
    at ave.a(SourceFile:310)
    at net.minecraft.client.main.Main.main(SourceFile:124)


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

-- Head --
Stacktrace:
    at bmi.a(SourceFile:230)
    at bmh.b(SourceFile:130)
    at bmh.a(SourceFile:77)
    at bot.j(SourceFile:553)
    at bot.a(SourceFile:139)
    at bou.a(SourceFile:23)
    at bnn.a(SourceFile:99)
    at ave.am(SourceFile:448)

-- Initialization --
Details:
Stacktrace:
    at ave.a(SourceFile:310)
    at net.minecraft.client.main.Main.main(SourceFile:124)

-- System Details --
Details:
    Minecraft Version: 1.8.7
    Operating System: Mac OS X (x86_64) version 10.9.5
    CPU: 2x Intel(R) Core(TM)2 Duo CPU P8600 @ 2.40GHz
    Java Version: 1.6.0_65, Apple Inc.
    Java VM Version: Java HotSpot(TM) 64-Bit Server VM (mixed mode), Apple Inc.
    Memory: 282712 bytes (0 MB) / 1060372480 bytes (1011 MB) up to 1060372480 bytes (1011 MB)
    JVM Flags: 5 total; -Xmx1G -XX:+UseConcMarkSweepGC -XX:+CMSIncrementalMode -XX:-UseAdaptiveSizePolicy -Xmn128M
    IntCache: cache: 0, tcache: 0, allocated: 0, tallocated: 0
    Launched Version: 1.8.7
    LWJGL: 2.9.2
    OpenGL: NVIDIA GeForce 320M OpenGL Engine GL version 2.1 NVIDIA-8.24.16 310.90.9.05f01, NVIDIA Corporation
    GL Caps: Using GL 1.3 multitexturing.
Using GL 1.3 texture combiners.
Using framebuffer objects because ARB_framebuffer_object is supported and separate blending is supported.
Shaders are available because OpenGL 2.1 is supported.
VBOs are available because OpenGL 1.5 is supported.

    Using VBOs: Yes
    Is Modded: Probably not. Jar signature remains and client brand is untouched.
    Type: Client (map_client.txt)
    Resource Packs: [PureBDcraft 512x MC18, herobrinepack9110877]
    Current Language: English (US)
    Profiler Position: N/A (disabled)

And this is the text Mojang/Minecraft shows me all the time!

Uhoh, it looks like the game has crashed! Sorry for the inconvenience.

With magic and love (?) we've managed to grab some details about the crash and >we will get on it as soon as we can You can see the full crash below

Can anyone here help me? It would mean the world to me!