Core Image custom filter to generate an angular gradient. The center is at the origin (0,0). You may want to use CIAffineTransform and/or CICrop on the output.

PRHAngleGradientFilter.h

//
//  PRHAngleGradientFilter.h
//
//  Created by Peter Hosey on 2013-01-30.
//  Copyright (c) 2013 Peter Hosey. All rights reserved.
//

#import <QuartzCore/QuartzCore.h>

@interface PRHAngleGradientFilter : CIFilter

@property(strong) CIColor *inputStartColor;
@property(strong) CIColor *inputMidColor;
@property(strong) CIColor *inputEndColor;

- (CIImage *) outputImage;

@end

PRHAngleGradientFilter.m

//
//  PRHAngleGradientFilter.m
//
//  Created by Peter Hosey on 2013-01-30.
//  Copyright (c) 2013 Peter Hosey. All rights reserved.
//

#import "PRHAngleGradientFilter.h"

@implementation PRHAngleGradientFilter
{
	CIKernel *_kernel;
}

- (id) init {
	if ((self = [super init])) {
		NSString *kernelText = @"kernel vec4 coreImageKernel(__color startColor, __color midColor, __color endColor)\n"
			"{\n"
			"\tvec2 point = destCoord();\n"
			"\n"
			"\tfloat angle = atan(point.y, point.x) + radians(180.0);\n"
			"\t//Start from the upper middle, not the left middle\n"
			"\tangle += radians(90.0);\n"
			"\tangle = mod(angle, radians(360.0));\n"
			"\n"
			"\tfloat fraction = angle / radians(360.0);\n"
			//"\tfraction = clamp(fraction, 0.0, 1.0);\n"
			"\n"
			"\tvec4 resultColor = fraction < 0.5\n"
			"\t\t? startColor * (1.0 - fraction * 2.0) + midColor * (fraction * 2.0)\n"
			"\t\t: midColor * (1.0 - (fraction - 0.5) * 2.0) + endColor * ((fraction - 0.5) * 2.0);\n"
			"\treturn resultColor;\n"
			"}";
		_kernel = [CIKernel kernelsWithString:kernelText][0];
	}

	return self;
}

- (NSDictionary *) attributes {
	NSDictionary *attributes = @{
		kCIAttributeFilterCategories: @[
			kCICategoryColorAdjustment,
			kCICategoryVideo,
			kCICategoryStillImage,
			kCICategoryGenerator,
			kCICategoryGradient
		],
		kCIAttributeFilterName: @"PRHAngleGradientFilter",
		kCIAttributeFilterDisplayName: NSLocalizedString(@"Angle gradient", @"Localized name of PRHAngleGradientFilter"),

		@"inputStartColor": @{
			kCIAttributeClass: @"CIColor",
			kCIAttributeType: kCIAttributeTypeOpaqueColor,
			kCIAttributeDefault: [CIColor colorWithCGColor:CGColorGetConstantColor(kCGColorWhite)]
		},
		@"inputMidColor":  @{
			kCIAttributeClass: @"CIColor",
			kCIAttributeType: kCIAttributeTypeOpaqueColor,
			kCIAttributeDefault: [CIColor colorWithCGColor:CGColorGetConstantColor(kCGColorBlack)]
		},
		@"inputEndColor":  @{
			kCIAttributeClass: @"CIColor",
			kCIAttributeType: kCIAttributeTypeOpaqueColor,
			kCIAttributeDefault: [CIColor colorWithCGColor:CGColorGetConstantColor(kCGColorWhite)]
		},

		kCIOutputImageKey: @{
			kCIAttributeClass: @"CIImage"
		}
	};
	return attributes;
}

//Because Apple's implementations don't auto-detect input and output keys for us.
- (NSArray *) inputKeys {
	return [[super inputKeys]
		arrayByAddingObjectsFromArray:[self.attributes.allKeys filteredArrayUsingPredicate:[NSPredicate predicateWithBlock:^BOOL(
			id evaluatedObject, NSDictionary *bindings
		) {
			return [evaluatedObject hasPrefix:@"input"];
		}]]];
}

- (NSArray *) outputKeys {
	return [[super outputKeys]
		arrayByAddingObjectsFromArray:[self.attributes.allKeys filteredArrayUsingPredicate:[NSPredicate predicateWithBlock:^BOOL(
			id evaluatedObject, NSDictionary *bindings
		) {
			return [evaluatedObject hasPrefix:@"output"];
		}]]];
}

- (CIImage *) outputImage {
	NSArray *args = @[
		[self valueForKey:@"inputStartColor"], [self valueForKey:@"inputMidColor"], [self valueForKey:@"inputEndColor"]
	];
	CIImage *outputImage = [self apply:_kernel arguments:args options:nil];
	return outputImage;
}

@end