From the course: Deke's Techniques (2018-2021)
742 Types 9, 11, 12, and 13: The Rice pentagons
From the course: Deke's Techniques (2018-2021)
742 Types 9, 11, 12, and 13: The Rice pentagons
- [Instructor] In this movie we'll look at types nine, 11, 12, and 13 of the guaranteed to tessellate perfectly irregular convex pentagons. And to see what they look like, I'll go ahead and click at this down pointing arrow head in the bottom left corner of the screen here inside the illustrator, the one labeled Artboard Navigation and I'll scroll down to this guy right here, Type 9. So again, types nine and 10 are out of order for reasons I do not know. But I'll just go ahead and choose Type 9 which happens to be on Artbard 16 in order to see the first of four pentagons discovered by Marjorie Rice in 1977. And this is a woman by the way, who had nothing more than a high school education and yet she was able to figure out more of these than anyone but that first guy Karl Reinhardt back in 1918. Alright so once again the angles up here in bold and the sides appear in italics, and we've got these rules. So, where the angles are concerned, 2A plus C is the same as D plus 2E which adds up to 360 degrees. Which as we'll see proves to be a little bit challenging. And once again, all of the sides except A are the very same length. So B equals C which equals D and E which means that these sides can abut each other. And to see what that looks like, I'll go ahead and switch back to my layers panel and I'll turn on my patterns layer so that we can see that the tile ends up repeating a total of eight times, which is why we have eight different colors on screen. And to see how I assembled things, which took a little bit of effort, I'll turn on a couple of more layers here. And notice this is the original shape colored in light blue, I went ahead and flipped it across the vertical axis so that amounts to a horizontal flip and then I rotated it 46.63 degrees which happens to suite this specific shape quite nicely. And then, I went ahead and took both of these shapes and rotated copies of them 78.85 degrees. And so why these values are working, I really don't know, I just know that they ended up making everything fit perfectly. Then, I took all four of these shapes and I flipped them across the horizontal axis so in other words, a vertical flip and then I rotated them all 125.48 degrees in order to create these orange shapes right there and then I dragged around a bunch of copies in order to create this manual pattern. Alright, I'm gonna go ahead and turn off that patterns layer and I'll press Shift Page Down in order to advance to the next Artboard which takes us from Type 9 to Type 11, once again created by Marjorie Rice. This time around we have more of an elongated shape, in which angle A is exactly 90 degrees. So we've got a right angle at this location. Then 2B plus C equals 360 degrees and C plus E equals 180 degrees. Which by the way, may possibly exceed my ability to visualize at this point, but we have side D equaling side E, so they're exactly the same length, which also happens to equal 2A plus C, which is why I've colored side A in orange and you can see there's A against E. There's another A against E, so a second instance and then we have C colored in green in between. And we're seeing the same thing against side D. If you're interested in how this shakes out, I'll go ahead and turn on the patters layer once again and we end up with these kind of fish faces biting each other. Once again, I'm duplicating the base tile a total of eight times. And to make that happen, I went ahead and took that first shape and I flipped it across the H axis. So quite obviously we have a vertical flip and then I took those two shapes and I flipped them across the vertical axis in order to produce a horizontal flip. So at least where these four shapes are concerned, it's pretty easy. And then I took block one, which I'm calling these two shapes right here, and I rotated them negative 58.79 degrees in order to fit these two shapes into this location. And then I took these two block two shapes and rotated copies of them by the very same amount, negative 58.97 degrees and I ended up with this more or less perfect fit right here. Alright, I'll go ahead and turn off those layers and I'll advance to the next Artboard so we can see Type 12, which has some very similar rules. So all the angles shake out the same, that is to say just like before. So notice this is Type 11, this is Type 12. A is equal to exactly 90 degrees, so a right angle, 2B plus C, whatever they are equal 360 degrees and then C and E, which can vary as long as they together equal 180 degrees. This time D, this side right here, is equal to 2A, so two times A, which is colorized in red. The reason we're seeing green and orange against side D is because it's also equal to C plus E, so C is green and E is orange. Which means all these sides compile up against each other as witnessed in this pattern right here. And so we have these kind of fish faces once again but they're biting each other at different angles. So this is Type 11, just to refresh your memory and this is Type 12. And so to assemble this pattern I came up with this approach, you might try things differently. But I started with this original shape, I flipped it vertically, so across the horizontal axis and then I flipped them both across the vertical axis, so horizontally, which is to say I started things in exactly the same way but then I took the entire group, so I didn't approach it one block at a time like before, I took all of the shapes and I flipped them across a horizontal access, so vertically and then I rotated them 62.53 degrees, ended up working out. Alright, I'll go ahead and turn those layers off and we'll advance to the final Marjorie Rice pentagon which is Type 13 right here. This time the angles shape out differently. So we've got B equals E equals 90 degrees so both B and E are right angles. And then, 2A plus D equals 360 degrees, whatever on that one, but where the sides are concerned D equals 2A which also equals 2E. So in other words, sides A and E are exactly equal to each other and then if you multiply either one of them times two you end up with side D. And that looks pretty regular as we're seeing right here, so notice that we're getting some extremely horizontal and vertical alignment out of our repeated shapes, which one again, add up to eight. So in other words, I took the first one and duplicated it a total of seven times. Which looks like this right here. So here's our original shape, I flipped it vertically across the horizontal axis, I flipped both of them horizontally, so across the vertical axis and then I took all four and all I had to do this time was rotate them exactly 90 degrees, presumably because we've got those right angles. Now you may not really care for this perpendicular orientation, in which case, just go ahead and click anywhere inside that pattern in order to select the entire thing and then go up to the Effect menu, choose Distort & Transform and choose the Transform command which will allow us to rotate the pattern dynamically. And so I'll go ahead and choose a command, if you get this alert message telling you that I've already applied some transform effects, just go ahead and click Apply New Effect in order to bring up the Transform dialog box. Then, turn on the preview checkbox, very important, so you can see what you're doing, click in a rotate angle value and press shift up arrow, maybe a couple of times in order to rotate the entire pattern 20 degrees. Now these are actually path outlines, so go ahead and leave the transform objects checkbox turned on at which point you can click OK in order to apply that effect. And there you have it, four more types added to the pantheon of perfectly tessellating, irregular convex pentagons as discovered by Marjorie Rice, a mom who had no more than a high school education, doing much better than I would with my Bachelor's Degree in response to a Scientific American article back in 1977.
Practice while you learn with exercise files
Download the files the instructor uses to teach the course. Follow along and learn by watching, listening and practicing.
- 669_custom_QR.zip
- 670_more_QR.zip
- 671_hidden_circles.zip
- 673_shade_panels.zip
- 672_more_rectangles.zip
- 674_cafe_wall.zip
- 675_skewed_walls.zip
- 676_magic_checkers.zip
- 677_magic_dots.zip
- 678_reverse_illusion.zip
- 679_illusion_decor.zip
- 680_more_gizmos.zip
- 681_connect_gizmos.zip
- 682_wifi_symbol.zip
- 683_bluetooth_logo.zip
- 684_trajan_color.zip
- 685_trajan_AIcc.zip
- 686_stylistic_PsCC.zip
- 687_stylistic_AIcc.zip
- 688_grad_molecules.zip
- 689_sharper_moles.zip
- 690_smart_cules.zip
- 691_explore_cules.zip
- 692_blend_cules.zip
- 693_high_pass_cules.zip
- 694_cell_pattern.zip
- 695_hemoglobin.zip
- 696_edgy_cells.zip
- 697_springy_cells.zip
- 698_accordian_letters.zip
- 699_skew_blends.zip
- 700_cross_blends.zip
- 701_slice_blend.zip
- 702_blend_distort.zip
- 703_dynamic_roughen.zip
- 704_fish_twist.zip
- 705_dynam_bgnd_1.zip
- 706_dynam_bgnd_2.zip
- 707_quieter_art.zip
- 708_disintegration.zip
- 709_more_flakes.zip
- 710_mask_ashes.zip
- 711_flakes_to_ash.zip
- 712_note_tool.zip
- 713_contour_map.zip
- 714_contour_grad.zip
- 715_contour_arb.zip
- 716_contour_riff.zip
- 717_smooth_contour.zip
- 718_contour_cash.zip
- 719_color_of_money.zip
- 720_AI_adjust.zip
- 721_computer_key.zip
- 722_key_type.zip
- 723_faux_hedcut.zip
- 724_hedcut_lines.zip
- 725_color_hedcut.zip
- 726_ET_moon.zip
- 727_ET_trees.zip
- 728_ET_TRex.zip
- 729_global_glow.zip
- 730_content_aware.zip
- 731_space_portal.zip
- 732_enhance_portal.zip
- 733_rushing_stars.zip
- 734_AIcc_puppet.zip
- 735_puppet_tricks.zip
- 736_complex_puppet.zip
- 737_puppet_shortcut.zip
- 738_pentagons.zip
- 739_reinhardt.zip
- 740_kershner.zip
- 741_james_pentagon.zip
- 742_rice_pentagons.zip
- 743_stein_pentagon.zip
- 744_15th_pentagon.zip
- 745_tessellate_15.zip
- 746_pentatiles.zip
- 747_mod_pattern.zip
- 748_complement_tiles.zip
- 749_image_pattern.zip
- 750_pattern_fit.zip
- 751_candy_keeper.zip
- 752_keeper_text.zip
- 753_monster_movie.zip
- 754_mono_halftone.zip
- 755_word_haunted.zip
- 756_cheat_letters.zip
- 757_alt_adjust.zip
- 758_scuba_mono.zip
- 759_backscatter.zip
- 760_sample_outside.zip
- 761_Ps_vector_logo.zip
- 762_trans_shapes.zip
- 763_photo_logo.zip
- 764_high_res_snow.zip
- 765_enhance_snow.zip
- 766_snowflake_bokeh.zip
- 767_mandala_ps.zip
- 768_mandala_pattern.zip
- 769_mandala_dots.zip
- 770_mandala_color.zip
- 771_mandala_final.zip
- 772_AI_trim_view.zip
- 773_AI_presentation.zip
- 774_global_edits.zip
- 775_global_control.zip
- 776_freeform_grads.zip
- 777_freeform_lines.zip
- 778_freeform_gotcha.zip
- 779_great_white.zip
- 780_sharper_shark.zip
- 781_vibrance_sat.zip
- 782_vib_sat_sharp.zip
- 783_hedcut_action.zip
- 784_action_actions.zip
- 785_color_lines.zip
- 786_combine_lines.zip
- 787_clip_to_group.zip
- 788_color_outside.zip
- 789_flip_horizontal.zip
- 790_white_walker.zip
- 791_walker_begins.zip
- 792_digital_shave.zip
- 793_deep_wrinkles.zip
- 794_deep_brows.zip
- 795_pale_lips.zip
- 796_glowing_blue.zip
- 797_lifeless_pupils.zip
- 798_cold_gloomy.zip
- 799_brittle_flakes.zip
- 800_trans_shapes.zip
- 801_range_mask.zip
- 802_flip_photo.zip
- 803_actual_dream.zip
- 804_augment_dream.zip
- 805_smart_distortions.zip
- 806_blend_distortions.zip
- 807_star_negative.zip
- 808_star_pattern.zip
- 809_shaded_stars.zip
- 810_grad_pattern.zip
- 811_pattern_fade.zip
- 813_gobstopper.zip
- 814_gobpattern.zip
- 815_galignment.zip
- 816_etched_lines.zip
- 817_blend_pattern.zip
- 818_cubical_holes.zip
- 819_grad_pattern.zip
- 820_iso_arrows.zip
- 821_position_tips.zip
- 822_fill_gaps.zip
- 823_cartoon_teeth.zip
- 824_triangle_eye.zip
- 825_add_windows.zip
- 826_perfect_tessellate.zip
- 827_triangle_tunnels.zip
- 828_triangles_pattern.zip
- 829_colorful_triangles.zip
- 830_recolor_triangles.zip
- 831_rainbow_blends.zip
- 832_pattern_blends.zip
- 833_imposs_trident.zip
- 834_shade_trident.zip
- 835_opposing_grads.zip
- 836_trident_shadows.zip
- 837_impossible_hex.zip
- 838_impossible_lattice.zip
- 839_Joan_Miro.zip
- 840_watercolor_wash.zip
- 841_Miro_signature.zip
- 842_Photoshop_Miro.zip
- 843_enlarge_Miro.zip
- 844_Miro_Peele.zip
- 845_color_Us.zip
- 846_red_rorschach.zip
- 847_finish_Us.zip
- 848_CAF_fails.zip
- 849_turkey_2019.zip
- 850_trace_hand.zip
- 851_articulated_hand.zip
- 852_colorful_hand.zip
- 853_paint_fingernails.zip
- 854_paint_turkey.zip
- 855_turkey_feathers.zip
- 856_drop_shadow.zip
- 857_Ps_iPad_1.zip
- 858_Ps_iPad_2.zip
- 859_Ps_iPad_3.zip
- 860_iPad_Sidecar.zip
- 861_Adobe_Fresco.zip
- 862_Fresco_halftones.zip
- 863_live_brushes.zip
- 864_oil_paint.zip
- 865_Fresco_masks.zip
- 866_repurpose_mask.zip
- 867_vector_brush.zip
- 868_fresco_ps.zip
- 869_auto_color.zip
- 870_ACR_pano.zip
- 871_correct_pano.zip
- 872_diffusion.zip
- 873_simplify_2020.zip
- 874_fill_gaps.zip
- 875_posterize.zip
- 876_paint_bucket.zip
- 877_nonD_poster.zip
- 878_dynamic_poster.zip
- 879_filmstrip.zip
- 880_awful_awesome.zip
- 881_rembrandt.zip
- 882_recolor_freeform.zip
- 883_recolor_group.zip
- 884_over_under.zip
- 885_dev_over_under.zip
- 886_3D_metal_star.zip
- 887_heavy_metal.zip
- 888_wonder_poster.zip
- 889_wonder_displace.zip
- 890_wonder_woman.zip
- 891_metadata_template.zip
- 892_edit_metadata.zip
- 893_quilt_warp.zip
- 894_warp_object.zip
- 895_gopro_images.zip
- 896_content_aware.zip
- 897_gopro_combo.zip
- 898_blend_vignette.zip
- 899_photo_painting.zip
- 900_cue_ball.zip
- 901_pool_ball.zip
- 902_stripe_ball.zip
- 903_transform_each.zip
- 904_recolor_pool.zip
- 905_pool_cues.zip
- 906_rotate_cues.zip
- 907_repeat_face.zip
- 908_rainbow_faces.zip
- 909_mask_lips.zip
- 910_single_many.zip
- 911_symmetrical_mask.zip
- 912_colorize_grads.zip
- 913_mask_grads.zip
- 914_lantern_type1.zip
- 915_lantern_type2.zip
- 916_lantern_type3.zip
- 917_blend_steps.zip
- 918_blended_blends.zip
- 919_reverse_order.zip
- 920_pattern_colors.zip
- 921_blend_pattern.zip
- 922_polygons.zip
- 923_equil_triangle.zip
- 924_mercedes.zip
- 925_star_ring.zip
- 926_perfect_star.zip
- 927_lets_review.zip
- 928_basic_shapes.zip
- 929_triangle_man.zip
- 930_paint_grads.zip
- 931_adv_grads.zip
- 932_trans_vectors.zip
- 933_free_distort.zip
- 934_dynamic_fx.zip
- 935_cats_eye.zip
- 936_cat_iris.zip
- 937_primitives.zip
- 938_zig_zag.zip
- 939_dynamic_hilight.zip
- 940_reptile_scales.zip
- 941_shade_eye.zip
- 942_variable_shade.zip
- 943_dragon_eye.zip
- 945_single_thumbnail.zip
- 946_ai_home.zip
- 947_unlock_object.zip
- 948_unlock_icon.zip
- 949_line_tool.zip
- 950_broken_candy.zip
- 951_candy_rhino.zip
- 952_wrap_pattern.zip
- 953_ice_shadows.zip
- 954_illustrator_ipad.zip
- 955_pencil_points.zip
- 956_ipad_blob.zip
- 957_ipad_pen.zip
- 958_grads_repeats.zip
- 959_color_grading.zip
- 960_grading_tricks.zip
- 961_blend_balance.zip
- 962_font_height.zip
- 963_camera_profile.zip
- 964_JPEG_raw.zip
- 965_match_detail.zip
- 966_Ps_line_tool.zip
- 967_troubleshoot_line.zip
- 968_blend_vectors.zip
- 969_curve_line.zip
- 970_point_glyphs.zip
- 971_area_glyphs.zip
- 972_snap_glyphs.zip
- 973_snap_letterform.zip
- 974_glyph_shape.zip
- 975_glyph_pen.zip
- 976_playing_cards.zip
- 977_scale_shape.zip
- 978_card_suits.zip
- 979_enhance_path.zip
- 980_power_symbol.zip
- 981_huge_artboard.zip
- 982_new_artboard.zip
- 983_triceratops.zip
- 984_pen_tricks.zip
- 985_round_corner.zip
- 986_draw_round.zip
- 987_reshape_round.zip
- 988_AI_brushed.zip
- 989_AI_rivets.zip
- 990_blend_grad.zip
- 991_binoculars.zip
- 992_blue_halo.zip
- 993_bi_aberrations.zip
- 994_hide_shapes.zip
- 995_subwoofer.zip
- 996_deep_cone.zip
- 997_gradient_frame.zip
- 998_hex_screws.zip
- 999_thats_all.zip
Contents
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669 Customizing a QR code in Photoshop11m 22s
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670 Adding more color to your QR code4m 29s
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671 Coffer illusion and the hidden circles18m 10s
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672 Filling out the hidden circles illusion9m 30s
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673 Shading the panels in a Coffer illusion13m 1s
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674 Drawing a classic “café wall” illusion11m 20s
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675 Skewing your crazy café walls in Illustrator9m 25s
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676 Creating a “magical checkers” illusion20m 8s
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677 Swapping magical checkers for dots8m 35s
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678 Reversing the direction of your illusion8m 33s
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679 Decorating your illusion9m 47s
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680 Adding more and more gizmos11m 52s
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681 Connecting the gizmos wirelessly4m 59s
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682 Drawing a Wi-Fi symbol in Illustrator9m 48s
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683 Drawing the official Bluetooth logo10m 8s
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684 Introducing Trajan Color Concept13m 10s
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685 Trajan Color Concept in Illustrator CC7m 10s
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686 Using stylistic sets in Photoshop CC9m 37s
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687 Using stylistic sets in Illustrator CC6m 47s
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688 Creating gradient molecules in Photoshop10m 17s
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689 Sharpening your very soft molecules4m 41s
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690 Editing your smart-filtered molecules6m 32s
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691 Exploring regular molecule patterns17m 41s
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692 Blending opposing rows of colorful molecules8m 49s
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693 Sharpening molecules with High Pass6m 3s
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694 Creating shimmering cells in Illustrator12m 25s
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695 Turning regular hexagons into organic cells11m 50s
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696 Enhancing your organic cells in Photoshop8m 58s
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697 Making dead cells spring to life7m 41s
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698 Creating letters with accordion extrusions13m 58s
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699 Combining object blends with skews11m 28s
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700 Making one object blend cut through another9m 44s
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701 Making one object blend slice across another13m 27s
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702 Object blends and dynamic distortions in Illustrator8m 11s
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703 Another random distortion: Roughen7m 57s
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704 Dynamic warp distortions: Fish and Twist8m 52s
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705 Adding a dynamic background, part 110m 14s
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706 Adding a dynamic background, part 27m 44s
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707 “Quieting down” an overly elaborate design9m 25s
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708 The Marvel disintegration effect9m 14s
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709 Building up more flakes and ashes7m 33s
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710 Enhancing and masking your disintegration8m 12s
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711 Turning your flakes into dull, dead ash4m 10s
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712 Jogging your memory with the Note tool9m 59s
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713 Contour mapping with Distort > Displace10m 23s
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714 Contour map + gradient map6m 54s
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715 Contour map + arbitrary map8m 22s
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716 Riffing on a contour map in Photoshop5m 24s
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717 Smoothing out jagged contour lines4m 11s
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718 Contour mapping for cash in Photoshop9m 27s
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719 Infusing an image with the color of money2m 53s
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720 Simulating an adjustment layer in Illustrator9m 25s
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721 Drawing a stylish computer key12m 9s
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722 Spelling a word in computer keys6m 55s
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723 Creating a faux hedcut in Photoshop13m 7s
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724 Tracing outlines around your hedcut7m 47s
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725 Creating a full-color hedcut effect7m 32s
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726 Creating an E.T. moon in Photoshop8m 42s
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727 Adding a forest of trees for your E.T. moon10m 41s
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728 Combining the best of E.T. and Jurassic Park10m 59s
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729 Tracing vectors with a universal glow6m 17s
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730 Creative uses for Content-Aware Fill11m 47s
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731 Creating a porthole to a far-away galaxy7m 42s
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732 Enhancing your crazy space porthole7m 3s
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733 Creating a galaxy of rushing stars5m 42s
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734 Using the Puppet Warp tool in Illustrator CC6m 7s
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735 Illustrator Puppet Warp tips and tricks7m 20s
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736 Puppet-Warping very complicated selections6m 18s
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737 Shift-P for Puppet Warp!2m 59s
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738 Introducing the Pentagon Patterns7m 29s
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739 Types 1–5: The Reinhardt pentagons14m 17s
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740 Types 6–8: The Kershner pentagons5m 47s
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741 Type 10: The James pentagon5m 53s
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742 Types 9, 11, 12, and 13: The Rice pentagons7m 58s
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743 Type 14: The Stein pentagon3m 53s
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744 Creating a type 15 pentagon in Illustrator9m 27s
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745 Tessellating your type 15 pentagon14m 22s
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746 Expressing pentagons as proper tile patterns12m 9s
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747 Applying and modifying a tile pattern11m
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748 Combining complementary patterns7m 43s
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749 Combining a tile pattern with a photograph6m 33s
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750 Adjusting a tile pattern to fit its photo5m 36s
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751 Creating a creepy Candy Keeper in Photoshop3m 59s
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752 Enhancing the Candy Keeper text4m 46s
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753 Creating an old monster movie poster7m 3s
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754 Adding a monochrome halftone effect4m 3s
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755 Enhancing a special word, such as “Haunted”4m 27s
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756 Cheating letters into an ancient border2m 25s
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757 Naming an adjustment layer as you create it4m 13s
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758 Under the sea in strict monochrome6m 29s
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759 Backscatter and split toning7m 21s
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760 Sampling any color outside Photoshop3m 17s
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761 Designing a vector-based logo in Photoshop9m 20s
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762 Free-transforming shape layers7m 56s
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763 Adding a photo element to your vector logo6m 34s
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764 High-resolution snowflakes in Photoshop5m 45s
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765 Enhancing your big, juicy snowflakes7m 19s
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766 Adding a snowflake bokeh “on the lens”6m 8s
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